Deck 5: Circular Motion

Question 1

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular velocity of 25 radians per second, then the linear speed of a point on the circumference is

A) 1.0 m/s.
B) 1.5 m/s.
C) 2.0 m/s.
D) 2.5 m/s.
E) 3.0 m/s.

Answer 1

1.5 m/s.

Question 2

An object moving in a circle at a constant speed is

A) accelerating in the direction of motion.
B) accelerating toward the center of the circle.
C) accelerating away from the center of the circle.
D) not accelerating because its speed is constant.

Answer 2

accelerating toward the center of the circle.

Question 3

A CD has a diameter of 12.0 cm. If the CD is rotating with a constant period of 0.314 seconds, then the frequency of the rotational motion is

A) 4.00 Hz.
B) 3.67 Hz.
C) 3.18 Hz.
D) 2.83 Hz.
E) 2.15 Hz.

Answer 3

3.18 Hz.

Question 4

An object is moving in a circular path with a radius of 5.00 m. If the object moves through an angle of 270 degrees, then the tangential distance traveled by the object is

A) 4.71 m.
B) 15.2 m.
C) 23.6 m.
D) 40.2 m.

Question 5

A 4.00 kg mass is moving in a circular path with a constant angular speed of 5.00 rad/sec and with a linear speed of 5.00 m/sec. The magnitude of the radial force on the mass is

A) 90.0 N.
B) 100 N.
C) 125 N.
D) 169 N.
E) 200 N.

Question 6

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 3.18 Hz, then the period of the rotational motion is

A) 0.314 s.
B) 0.441 s.
C) 0.582 s.
D) 0.698 s.
E) 0.750 s.

Question 7

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 4.00 rotations per second, then the linear speed of a point on the circumference is

A) 1.25 m/s.
B) 1.31 m/s.
C) 1.51 m/s.
D) 1.82 m/s.
E) 2.00 m/s.

Question 8

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 20 radians per second, then the linear speed of a point on the circumference is

A) 2.0 m/s.
B) 1.9 m/s.
C) 1.5 m/s.
D) 1.2 m/s.
E) 1.0 m/s.

Question 9

An object is moving in a circular path of radius 4.00 m. If the object moves through an angle of 30.0 degrees, then the tangential distance traveled by the object is

A) 3.66 m.
B) 3.21 m.
C) 2.84 m.
D) 2.09 m.
E) 1.75 m.

Question 10

An object is moving in a circular path of radius R. If the object moves through an angle of 30 degrees, then the angle in radians is

A) 0.22 radians.
B) 0.52 radians.
C) 0.75 radians.
D) 1.30 radians.
E) 1.75 radians.

Question 11

An object is moving in a circular path of radius 4.00 m. If the object moves through a tangential distance of 3.00 meters, then the angle the object travels through is

A) 0.750 radians.
B) 1.05 radians.
C) 1.46 radians.
D) 1.75 radians.
E) 1.90 radians.

Question 12

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 200 revolutions per minute, then the linear speed of a point on the circumference is

A) 1.06 m/s.
B) 1.26 m/s.
C) 1.39 m/s.
D) 1.62 m/s.
E) 1.32 m/s.

Question 13

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 20.0 radians per second, then the frequency of the rotational motion is

A) 2.14 Hz.
B) 3.18 Hz.
C) 3.83 Hz
D) 4.50 Hz.
E) 4.89 Hz.

Question 14

A 4.00 kg mass is moving in a circular path of radius 2.50 m with a constant angular speed of 5.00 rad/sec. The magnitude of the radial force on the mass is

A) 250 N.
B) 185 N.
C) 153 N.
D) 107 N.
E) 94.0 N.

Question 15

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 4.00 rotations per second, then the period of the rotational motion is

A) 0.250 s.
B) 0.500 s.
C) 0.750 s.
D) 1.00 s.
E) 1.25 s.

Question 16

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 6.00 rotations per second, then the angular speed is

A) 21.5 rad/s.
B) 26.9 rad/s.
C) 29.6 rad/s.
D) 33.3 rad/s.
E) 37.7 rad/s.

Question 17

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 20.0 radians per second, then the period of the rotational motion is

A) 0.143 s.
B) 0.224 s.
C) 0.314 s.
D) 0.421 s.
E) 0.558 s.

Question 18

An object is moving in a circular path of radius 4.00 m. If the object moves through an angle of 1.2 radians, then the tangential distance traveled by the object is

A) 2.8 m.
B) 3.2 m.
C) 3.8 m.
D) 4.3 m.
E) 4.8 m.

Question 19

A 4.0 kg mass is moving in a circular path of radius 2.5 m with a constant linear speed of 5.0 m/s. The magnitude of the radial force on the mass is

A) 20 N.
B) 25 N.
C) 35 N.
D) 40 N.
E) 45 N.

Question 20

An object is moving in a circular path with a radius of 4.0 m. If the object moves through an angle of 45 degrees, then the angle in radians is

A) 0.25 radians.
B) 0.53 radians.
C) 0.79 radians.
D) 1.02 radians.
E) 1.44 radians.

Question 21

A 5,000 kg satellite is orbiting the Earth in a circular path. The height of the satellite above the surface of the Earth is 800 km. The angular speed of the satellite as it orbits the Earth is (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 9.50 × 10⁻⁴ rad/s.
B) 1.04 × 10⁻³ rad/s.
C) 1.44 × 10⁻³ rad/s.
D) 1.90 × 10⁻³ rad/s.
E) 2.20 × 10⁻³ rad/s.

Question 22

An airplane is traveling at 150 m/s in level flight. In order to make a change in direction, the airplane travels in a horizontal curved path. To fly in the curved path, the pilot banks the airplane at an angle such that the lift has a horizontal component that provides the horizontal radial acceleration to move in a horizontal circular path. If the airplane is banked at an angle of 12.0 degrees, then the radius of curvature of the curved path of the airplane is

A) 10.8 km.
B) 8.74 km.
C) 8.00 km.
D) 7.33 km.
E) 6.90 km.

Question 23

A 5,000 kg satellite is orbiting the Earth in a geostationary orbit. The height of the satellite above the surface of the Earth is (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 8.29 × 10⁷ m.
B) 6.35 × 10⁷ m.
C) 3.59 × 10⁷ m.
D) 2.95 × 10⁷ m.
E) 1.40 × 10⁷ m.

Question 24

A 2.60 kg mass is moving in a circular path with a constant angular speed of 5.50 rad/sec and with a linear speed of 3.50 m/s. The magnitude of the radial force on the mass is

A) 30.4 N.
B) 40.5 N.
C) 50.1 N.
D) 60.5 N.
E) 66.7 N.

Question 25

A 1.00 kg stone attached to a 1.00 m long string is traveling in a vertical circular path. What is the minimum linear speed needed at the top of the circle to keep the string from going slack?

A) 5.63 m/s
B) 5.31 m/s
C) 5.00 m/s
D) 4.50 m/s
E) 3.13 m/s

Question 26

A conical pendulum is constructed by attaching a mass to a string 2.00 m in length. The mass is set in motion in a horizontal circular path about the vertical axis. If the angle the string makes with the vertical axis is 45.0 degrees, then the angular speed of the conical pendulum is

A) 4.00 rad/s.
B) 3.55 rad/s.
C) 3.04 rad/s.
D) 2.63 rad/s.
E) 2.01 rad/s.

Question 27

A conical pendulum is constructed by attaching a mass to a string 2.5 m in length. The mass set in motion in a horizontal circular path about the vertical axis. If the angular speed of the conical pendulum is a constant 2.8 rad/s, then the angle the string makes with the vertical axis is

A) 48 degrees.
B) 60 degrees.
C) 71 degrees.
D) 75 degrees.
E) 80 degrees.

Question 28

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the linear speed of a point 4.0 cm from the center at the time 2.0 seconds from the start?

A) 0.060 m/s
B) 0.080 m/s
C) 0.10 m/s
D) 0.14 m/s
E) 0.18 m/s

Question 29

A 4.00 kg mass is moving in a circular path of radius 3.20 m with a constant linear speed of 6.20 m/s. The radial force on the mass is

A) 40.2 N away from the center.
B) 48.1 N toward the center.
C) 50.5 N away from the center.
D) 59.0 N toward the center.
E) 62.3 N away from the center.

Question 30

A 4.00 kg mass is moving in a circular path of radius 4.10 m with a constant angular speed of 5.00 rad/sec. The radial force on the mass is

A) 267 N toward the center.
B) 294 N toward the center.
C) 302 N toward the center.
D) 350 N toward the center.
E) 410 N toward the center.

Question 31

A 2000 kg car is traveling on a banked, curved, icy road. The speed of the car is 25.0 m/s and the road has a radius of curvature of 500 m. If the car is to travel on the icy road without sliding, then the angle of the banked road should be

A) 25.7 degrees.
B) 21.0 degrees.
C) 12.7 degrees.
D) 10.5 degrees.
E) 7.27 degrees.

Question 32

A 0.500 kg stone is moving in a vertical circular path attached to a string that is 75.0 cm long. The stone is moving around the path at a constant frequency of 1.50 rev/sec. At the moment the stone is overhead, the stone is released. The speed of the stone when it leaves the circular path is

A) 5.55 m/s.
B) 7.07 m/s.
C) 7.75 m/s.
D) 8.35 m/s.
E) 9.00 m/s.

Question 33

A 2000 kg car is traveling on a curved, icy road without sliding. The speed of the car is 30 m/s and the road is banked at an angle of 20.0 degrees. The radius of curvature of the road is

A) 175 m.
B) 204 m.
C) 252 m.
D) 302 m.
E) 375 m.

Question 34

A 5,000 kg satellite is orbiting the Earth in a circular path. The height of the satellite above the surface of the Earth is 800 km. The speed of the satellite is (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 7,460 m/s.
B) 6,830 m/s.
C) 6,430 m/s.
D) 5,950 m/s.
E) 5,350 m/s.

Question 35

An airplane is traveling at 250 m/s in level flight. In order to make a change in direction, the airplane travels in a horizontal curved path. To fly in the curved path, the pilot banks the airplane at an angle such that the lift has a horizontal component that provides the horizontal radial acceleration to move in a horizontal circular path. If the airplane is banked at an angle of 15.0 degrees, then the radius of curvature of the curved path of the airplane is

A) 20.1 km.
B) 23.8 km.
C) 25.0 km.
D) 27.5 km.
E) 30.1 km.

Question 36

A 2000 kg car is traveling on a curved, icy road without sliding. The velocity of the car is 32.0 m/s and the road is banked at an angle of 20.0 degrees. The radius of curvature of the road is

A) 125 m.
B) 210 m.
C) 287 m.
D) 310 m.
E) 350 m.

Question 37

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete one orbit?

A) 320 days
B) 160 days
C) 20 days
D) 80 days

Question 38

A 5,000 kg satellite is orbiting the Earth in a circular path. The height of the satellite above the surface of the Earth is 800 km. The time it takes for the satellite to travel around the Earth is (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 0.750 hours.
B) 0.950 hours.
C) 1.25 hours.
D) 1.68 hours.
E) 2.01 hours.

Question 39

A 0.500 kg stone is moving in a vertical circular path attached to a string that is 75.0 cm long. The stone is moving around the path at a constant frequency of 2.20 rev/sec. At the moment the stone is overhead, the stone is released. The velocity of the stone when it leaves the circular path is

A) 10.4 m/s horizontal.
B) 10.4 m/s vertical.
C) 22.0 m/s horizontal.
D) 22.0 m/s vertical.
E) 31.4 m/s horizontal.

Question 40

A 2000 kg car is traveling on curved, icy road. The road is banked at an angle of 12.0 degrees and has a radius of curvature of 500 m. The speed of the car necessary to travel on the icy road without sliding is

A) 32.3 m/s.
B) 40.5 m/s.
C) 42.8 m/s.
D) 49.5 m/s.
E) 50.2 m/s.

Question 41

A CD has a diameter of 12.0 cm. If the CD starts from rest and has a constant angular acceleration of 2.00 rad/sec^2, then the radial acceleration of a point 3.00 cm from the center of the CD after 3.00 sec is

A) 0.950 m/s².
B) 1.08 m/s².
C) 1.25 m/s².
D) 1.58 m/s².
E) 1.83 m/s².

Question 42

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point 4.00 cm from the center, at the time 10.0 seconds from the start?

A) 27.6 rad
B) 37.5 rad
C) 40.7 rad
D) 48.2 rad
E) 51.2 rad

Question 43

A CD has a diameter of 12.0 cm. If the CD starts from rest and has a constant angular acceleration of 2.0 rad/sec², then the linear speed of a point 3.0 cm from the center of the CD after 3.0 sec is

A) 18 cm/s.
B) 21 cm/s.
C) 25 cm/s.
D) 32 cm/s.
E) 45 cm/s.

Question 44

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the magnitude of the (total) acceleration of a point 4.00 cm from the center at the time 30.0 seconds from the start?

A) 0.0650 m/s²
B) 0.0522 m/s²
C) 0.0444 m/s²
D) 0.0324 m/s²
E) 0.0243 m/s²

Question 45

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 2.0 seconds from the start?

A) 0.37 m/s²
B) 0.30 m/s²
C) 0.28 m/s²
D) 0.21 m/s²
E) 0.16 m/s²

Question 46

A CD has a diameter of 12.0 cm. If the CD starts from rest and has a constant angular acceleration of 2.0 rad/sec², then the angular velocity of the CD after 3.0 sec is

A) 12 rad/s.
B) 10 rad/s.
C) 9.0 rad/s.
D) 8.0 rad/s.
E) 6.0 rad/s.

Question 47

A CD has a diameter of 12.0 cm. If the CD starts from rest and has a constant angular acceleration of 2.0 rad/sec², then the tangential acceleration of a point 3.0 cm from the center of the CD after 3.0 sec is

A) 0.40 m/s².
B) 0.25 m/s².
C) 0.10 m/s².
D) 0.06 m/s².
E) 0.03 m/s².

Question 48

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point 4.0 cm from the center, at the time 2.0 seconds from the start?

A) 2.0 rad
B) 4.0 rad
C) 6.0 rad
D) 8.0 rad
E) 10.0 rad

Question 49

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 25.0 seconds from the start?

A) 0.47 m/s²
B) 0.40 m/s²
C) 0.34 m/s²
D) 0.24 m/s²
E) 0.20 m/s²

Question 50

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 10.0 seconds from the start?

A) 2.0 m/s²
B) 1.8 m/s²
C) 1.0 m/s²
D) 0.9 m/s²
E) 0.6 m/s²

Question 51

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the magnitude of the (total) acceleration of a point 4.00 cm from the center at the time 10.0 seconds from the start?

A) 0.65 m/s²
B) 1.00 m/s²
C) 1.25 m/s²
D) 1.37 m/s²
E) 1.86 m/s²

Question 52

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the linear speed of a point 4.0 cm from the center at the time 10.0 seconds from the start?

A) 0.50 m/s
B) 0.40 m/s
C) 0.30 m/s
D) 0.20 m/s
E) 0.10 m/s

Question 53

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point 4.00 cm from the center, at the time 25.0 seconds from the start?

A) 107 rad
B) 193 rad
C) 205 rad
D) 237 rad
E) 274 rad

Question 54

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the linear speed of a point 4.0 cm from the center at the time 25.0 seconds from the start?

A) 0.10 m/s
B) 0.017 m/s
C) 0.083 m/s
D) 0.00 m/s
E) 0.12 m/s

Question 55

A CD has a diameter of 12.0 cm. If the CD starts from rest and has a constant angular acceleration of 0.600 rad/sec², then the magnitude of the (total) acceleration of a point 3.00 cm from the center of the CD after 1.30 sec is

A) 0.0256 m/s².
B) 0.0306 m/s².
C) 0.0415 m/s².
D) 0.0472 m/s².
E) 0.0502 m/s².

Question 56

A CD has a diameter of 12.0 cm and is rotating at an angular velocity of 10.0 rad/sec. If the CD has a constant angular acceleration of −0.5 rad/sec², then the angular velocity of the CD after 3.0 sec is

A) 5.7 rad/s.
B) 6.2 rad/s.
C) 7.9 rad/s.
D) 8.5 rad/s.
E) 9.8 rad/s.

Question 57

A 2.0 kg mass is moving in a circular path with a radius of 5.00 cm. The mass starts from rest and, with constant angular acceleration, obtains an angular velocity of 6.00 rad/sec in 3.00 sec. The mass then comes to a stop with constant angular acceleration in 4.00 sec. The radial component of acceleration of the mass at 5.00 sec after the start is

A) 2.50 m/s².
B) 2.03 m/s².
C) 1.25 m/s².
D) 0.980 m/s².
E) 0.450 m/s².

Question 58

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 15.0 seconds from the start?

A) 0.5 m/s²
B) 1.0 m/s²
C) 1.8 m/s²
D) 2.0 m/s²
E) 2.6 m/s²

Question 59

A 2.00 kg mass is moving in a circular path with a radius of 5.00 cm. The mass starts from rest and, with constant angular acceleration, obtains an angular velocity of 6.00 rad/sec in 3.00 sec. The mass then comes to a stop with constant angular acceleration in 4.00 sec. The radial component of acceleration of the mass at 2.00 sec is

A) 1.220 m/s².
B) 0.980 m/s².
C) 0.800 m/s².
D) 0.656 m/s².
E) 0.100 m/s².

Question 60

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.00 rad/sec² acquires an angular velocity of 5.00 rad/sec. The CD continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the magnitude of the (total) acceleration of a point 4.00 cm from the center at the time 2.00 seconds from the start?

A) 0.450 m/s²
B) 0.314 m/s²
C) 0.215 m/s²
D) 0.165 m/s²
E) 0.100 m/s²

Question 61

The radius of the Earth is r. A satellite of mass 100 kg is at a point which is a distance 3r above the Earth's surface. What is the satellite's weight?

A) 6.3 N
B) 110 N
C) 61 N
D) 38 N

Question 62

A car travels at 17 m/s without skidding around a 35 m radius unbanked curve. What is the minimum value of the static friction coefficient between the tires and the road?

A) 0.84
B) 0.050
C) 0.0014
D) 0.024

Question 63

A car travels around a 35 m radius unbanked curve. The static friction coefficient between the tires and the road is 0.45. What is the maximum speed at which the car can travel without slipping around this curve?

A) 2.8 m/s
B) 27.6 m/s
C) 12.4 m/s
D) 7.5 m/s

Question 64

The Crab Pulsar is a neutron star, rotating with a period of about 33.085 ms. It is estimated to have an equatorial radius of 15 km, about average for a neutron star. The pulsar is slowing in its rotation so that it is expected to come to rest 9.5 × 10¹⁰ s in the future. What is the magnitude of the average angular acceleration in this situation?

A) 4.8 × 10⁻⁶ rad/s²
B) 3.0 × 10⁻⁵ rad/s²
C) 7.6 × 10⁻⁷ rad/s²
D) 2.0 × 10⁻⁹ rad/s²
E) 3.2 × 10⁻¹⁰ rad/s²

Question 65

The Crab Pulsar is a neutron star, rotating with a period of 33.085 ms. It is estimated to have an equatorial radius of 15 km, about average for a neutron star. What is the radial acceleration of an object on the surface at the equator of the pulsar?

A) 5.4 x 10⁸ m/s²
B) 2.7 x 10⁸ m/s²
C) 8.9 x 10⁸ m/s²
D) 6.7 x 10⁸ m/s²

Question 66

When a girl swings in a tire swing, the tangential acceleration in the rope

A) is the greatest at the highest point of the motion.
B) is the greatest at the lowest point of the motion.
C) is the greatest at a point neither highest nor lowest.
D) is constant.

Question 67

The Crab Pulsar is a neutron star, rotating with a period of about 33.085 ms. It is estimated to have an equatorial radius of 15 km, about average for a neutron star. The pulsar is slowing in its rotation so that it is expected to come to rest 9.5 × 10¹⁰ s in the future. Assuming it is slowing with a constant angular acceleration, what is the tangential acceleration of an object on the neutron star's equator?

A) 3.0 × 10⁻⁵ m/s²
B) 2.0 × 10⁻⁹ m/s²
C) 3.2 × 10⁻¹⁰ m/s²
D) 7.6 × 10⁻⁷ m/s²
E) 4.8 × 10⁻⁶ m/s²

Question 68

A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the magnitude of the acceleration of the marble as viewed by the observers inside the satellite? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 0.00 m/s²
B) 1.62 m/s²
C) 2.64 m/s²
D) 4.90 m/s²
E) 9.24 m/s²

Question 69

A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the magnitude of the acceleration of the marble as viewed by the observers on the Earth? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 9.80 m/s²
B) 9.24 m/s²
C) 8.90 m/s²
D) 8.62 m/s²
E) 7.95 m/s²

Question 70

A figure skater spins at the end of her routine and slows down with an angular acceleration of 1.2 radians per second squared. If she initially spun with a period of 0.2 seconds, how many turns does she go through while slowing to a stop?

A) 65
B) 6
C) 33
D) 15

Question 71

A car travels around an unbanked curve at 17 m/s. If the static friction coefficient between the tires and the road is 0.45, what is the minimum radius curve that the car can take at this speed without slipping?

A) 65 m
B) 3.9 m
C) 15 m
D) 8.1 m

Question 72

A planet of mass M orbits a star in a circular orbit of radius R, with orbital period T. What would be the orbital period of another planet, orbiting at radius R, but having mass 2M?

A) 0.71T
B) T
C) 1.4T
D) 2T
E) 0.50T

Question 73

A 35.0 kg child swings on a rope with a length of 6.50 m that is hanging from a tree. At the bottom of the swing the child is moving at a speed of 4.20 m/s. What is the tension in the rope?

A) 95.0 N
B) 438 N
C) 343 N
D) 366 N

Question 74

At what distance from the center of the Earth would one's weight be half that recorded on the Earth's surface? Let the Earth's radius be R.

A) 0.71R
B) 2R
C) 4R
D) 1.4R

Question 75

Two planets travel in circular orbits about a star at radii of r_a = 2R and r_b = R, respectively. What is the ratio of their periods T_a/T_b?

A) 1.6
B) 2.8
C) 1.3
D) 1.4
E) 2.0

Question 76

A roller coaster has a vertical loop with radius 29.5 m. What is the minimum speed of the roller coaster car at the top of the loop if the passengers do not lose contact with the seats?

A) 10.0 m/s
B) 14.0 m/s
C) 17.0 m/s
D) 19.0 m/s

Question 77

Two planets travel in circular orbits about a star. The period of planet A is T, while that of planet B is 3T. What is the ratio of their orbital radii, R_A/R_B?

A) 0.33
B) 0.19
C) 0.48
D) 0.69

Question 78

A circular space station (shaped like a big wheel) rotates to produce "artificial gravity". The apparent weight of an astronaut standing on the inside surface of the outer wall is equal to her weight on earth. The inside surface of the outer wall of the space station is 285 m from the axis of rotation. What is the period of rotation of the station?

A) 92 s
B) 34 s
C) 213 s
D) 183 s

Question 79

A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the force of gravity on the marble as viewed by the observers on the Earth? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A) 0.405 N
B) 0.362 N
C) 0.277 N
D) 0.202 N
E) 0.185 N

Question 80

A circular space station (shaped like a big wheel) rotates 100 times in one hour. The apparent weight of an astronaut standing on the inside surface of the outer wall is equal to her weight on earth. How far from the axis of rotation is the inside surface of the station's outer wall?

A) 322 m
B) 102 m
C) 56 m
D) 1012 m