Deck 5: Circular Motion

Question 1

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

A) $23.6 \mathrm{~m}$ .
B) $4.71 \mathrm{~m}$ .
C) $15.2 \mathrm{~m}$ .
D) $40.2 \mathrm{~m}$ .

Answer 1

$23.6 \mathrm{~m}$ .

Question 2

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

A) $1.75 \mathrm{~m}$
B) $2.09 \mathrm{~m}$ .
C) $2.84 \mathrm{~m}$ .
D) $3.66 \mathrm{~m}$ .
E) $3.21 \mathrm{~m}$ .

Answer 2

$2.09 \mathrm{~m}$ .

Question 3

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

A) $4.8 \mathrm{~m}$ .
B) $3.8 \mathrm{~m}$ .
C) $2.8 \mathrm{~m}$ .
D) $4.3 \mathrm{~m}$ .
E) $3.2 \mathrm{~m}$ .

Answer 3

$4.8 \mathrm{~m}$ .

Question 4

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant angular speed of 20.0 radians per second, then the period of the rotational motion is

A) $0.421 \mathrm{~s}$ .
B) $0.143 \mathrm{~s}$ .
C) $0.224 \mathrm{~s}$ .
D) $0.314 \mathrm{~s}$ .
E) $0.558 \mathrm{~s}$ .

Question 5

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant angular speed of 20.0 radians per second, then the frequency of the rotational motion is

A) $2.14 \mathrm{~Hz}$ .
B) $4.50 \mathrm{~Hz}$ .
C) $3.83 \mathrm{~Hz}$
D) $4.89 \mathrm{~Hz}$ .
E) $3.18 \mathrm{~Hz}$

Question 6

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant frequency of $3.18 \mathrm{~Hz}$ , then the period of the rotational motion is

A) $0.441 \mathrm{~s}$ .
B) $0.582 \mathrm{~s}$ .
C) $0.698 \mathrm{~s}$ .
D) $0.750 \mathrm{~s}$ .
E) $0.314 \mathrm{~s}$ .

Question 7

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $C D$ is rotating with a constant period of 0.314 seconds, then the frequency of the rotational motion is

A) $3.18 \mathrm{~Hz}$ .
B) $2.15 \mathrm{~Hz}$ .
C) $2.83 \mathrm{~Hz}$ .
D) $3.67 \mathrm{~Hz}$ .
E) $4.00 \mathrm{~Hz}$ .

Question 8

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant frequency of 4.00 rotations per second, then the period of the rotational motion is

A) $0.750 \mathrm{~s}$ .
B) $1.25 \mathrm{~s}$ .
C) $0.500 \mathrm{~s}$ .
D) $0.250 \mathrm{~s}$ .
E) $1.00 \mathrm{~s}$

Question 9

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant frequency of 4.00 rotations per second, then the linear speed of a point on the circumference is

A) $1.31 \mathrm{~m} / \mathrm{s}$ .
B) $2.00 \mathrm{~m} / \mathrm{s}$ .
C) $1.51 \mathrm{~m} / \mathrm{s}$ .
D) $1.25 \mathrm{~m} / \mathrm{s}$ .
E) $1.82 \mathrm{~m} / \mathrm{s}$

Question 10

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant frequency of 6.00 rotations per second, then the angular speed is

A) $26.9 \mathrm{rad} / \mathrm{s}$ .
B) $21.5 \mathrm{rad} / \mathrm{s}$ .
C) $37.7 \mathrm{rad} / \mathrm{s}$ .
D) $33.3 \mathrm{rad} / \mathrm{s}$ .
E) $29.6 \mathrm{rad} / \mathrm{s}$ .

Question 11

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

A) $250 \mathrm{~N}$ .
B) $107 \mathrm{~N}$ .
C) $94.0 \mathrm{~N}$ .
D) $153 \mathrm{~N}$ .
E) $185 \mathrm{~N}$ .

Question 12

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

A) $59.0 \mathrm{~N}$ toward the center.
B) $48.1 \mathrm{~N}$ toward the center.
C) $50.5 \mathrm{~N}$ away from the center.
D) $62.3 \mathrm{~N}$ away from the center.
E) $40.2 \mathrm{~N}$ away from the center.

Question 13

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

A) $50.1 \mathrm{~N}$ .
B) $66.7 \mathrm{~N}$ .
C) $30.4 \mathrm{~N}$ .
D) $40.5 \mathrm{~N}$ .
E) $60.5 \mathrm{~N}$ .

Question 14

An airplane is traveling at $150 \mathrm{~m} / \mathrm{s}$ 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) $8.74 \mathrm{~km}$ .
B) $6.90 \mathrm{~km}$
C) $7.33 \mathrm{~km}$ .
D) $10.8 \mathrm{~km}$
E) $8.00 \mathrm{~km}$ .

Question 15

An airplane is traveling at $250 \mathrm{~m} / \mathrm{s}$ 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) $27.5 \mathrm{~km}$ .
B) $23.8 \mathrm{~km}$ .
C) $30.1 \mathrm{~km}$
D) $20.1 \mathrm{~km}$
E) $25.0 \mathrm{~km}$ .

Question 16

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 $800 \mathrm{~km}$ . The speed of the satellite is $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11}\right.$ $\left.\mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

A) $5,950 \mathrm{~m} / \mathrm{s}$
B) $7,460 \mathrm{~m} / \mathrm{s}$ .
C) $6,430 \mathrm{~m} / \mathrm{s}$ .
D) $5,350 \mathrm{~m} / \mathrm{s}$ .
E) $6,830 \mathrm{~m} / \mathrm{s}$ .

Question 17

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 $800 \mathrm{~km}$ . The angular speed of the satellite as it orbits the Earth is $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37\right.$ $\times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}$ )

A) $1.04 \times 10^{-3} \mathrm{rad} / \mathrm{s}$ .
B) $1.44 \times 10^{-3} \mathrm{rad} / \mathrm{s}$ .
C) $9.50 \times 10^{-4} \mathrm{rad} / \mathrm{s}$ .
D) $2.20 \times 10^{-3} \mathrm{rad} / \mathrm{s}$ .
E) $1.90 \times 10^{-3} \mathrm{rad} / \mathrm{s}$ .

Question 18

A $5,000 \mathrm{~kg}$ satellite is orbiting the Earth in a geostationary orbit. The height of the satellite above the surface of the Earth is $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

A) $8.29 \times 10^{7} \mathrm{~m}$ .
B) $2.95 \times 10^{7} \mathrm{~m}$ .
C) $1.40 \times 10^{7} \mathrm{~m}$
D) $3.59 \times 10^{7} \mathrm{~m}$ .
E) $6.35 \times 10^{7} \mathrm{~m}$ .

Question 19

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 2.0 seconds from the start?

A) $0.18 \mathrm{~m} / \mathrm{s}$
B) $0.060 \mathrm{~m} / \mathrm{s}$
C) $0.080 \mathrm{~m} / \mathrm{s}$
D) $0.10 \mathrm{~m} / \mathrm{s}$
E) $0.14 \mathrm{~m} / \mathrm{s}$

Question 20

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 2.0 seconds from the start?

A) $0.21 \mathrm{~m} / \mathrm{s}^{2}$
B) $0.28 \mathrm{~m} / \mathrm{s}^{2}$
C) $0.30 \mathrm{~m} / \mathrm{s}^{2}$
D) $0.37 \mathrm{~m} / \mathrm{s}^{2}$
E) $0.16 \mathrm{~m} / \mathrm{s}^{2}$

Question 21

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ for $15 \mathrm{~seconds}$ and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point $4.0 \mathrm{~cm}$ from the center, at the time 2.0 seconds from the start?

A) $2.0 \mathrm{rad}$
B) $6.0 \mathrm{rad}$
C) $10.0 \mathrm{rad}$
D) $8.0 \mathrm{rad}$
E) $4.0 \mathrm{rad}$

Question 22

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 10.0 seconds from the start?

A) $0.6 \mathrm{~m} / \mathrm{s}^{2}$
B) $2.0 \mathrm{~m} / \mathrm{s}^{2}$
C) $0.9 \mathrm{~m} / \mathrm{s}^{2}$
D) $1.8 \mathrm{~m} / \mathrm{s}^{2}$
E) $1.0 \mathrm{~m} / \mathrm{s}^{2}$

Question 23

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ for $15.0 \mathrm{~seconds}$ and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point $4.00 \mathrm{~cm}$ from the center, at the time 10.0 seconds from the start?

A) $27.6 \mathrm{rad}$
B) $48.2 \mathrm{rad}$
C) $40.7 \mathrm{rad}$
D) $51.2 \mathrm{rad}$
E) $37.5 \mathrm{rad}$

Question 24

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 10.0 seconds from the start?

A) $0.20 \mathrm{~m} / \mathrm{s}$
B) $0.40 \mathrm{~m} / \mathrm{s}$
C) $0.50 \mathrm{~m} / \mathrm{s}$
D) $0.30 \mathrm{~m} / \mathrm{s}$
E) $0.10 \mathrm{~m} / \mathrm{s}$

Question 25

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 25.0 seconds from the start?

A) $0.47 \mathrm{~m} / \mathrm{s}^{2}$
B) $0.34 \mathrm{~m} / \mathrm{s}^{2}$
C) $0.40 \mathrm{~m} / \mathrm{s}^{2}$
D) $0.24 \mathrm{~m} / \mathrm{s}^{2}$
E) $0.20 \mathrm{~m} / \mathrm{s}^{2}$

Question 26

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The $\mathrm{CD}$ continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ 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 $4.00 \mathrm{~cm}$ from the center, at the time 25.0 seconds from the start?

A) $205 \mathrm{rad}$
B) $237 \mathrm{rad}$
C) $193 \mathrm{rad}$
D) $274 \mathrm{rad}$
E) $107 \mathrm{rad}$

Question 27

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 25.0 seconds from the start?

A) $0.00 \mathrm{~m} / \mathrm{s}$
B) $0.10 \mathrm{~m} / \mathrm{s}$
C) $0.017 \mathrm{~m} / \mathrm{s}$
D) $0.12 \mathrm{~m} / \mathrm{s}$
E) $0.083 \mathrm{~m} / \mathrm{s}$

Question 28

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The $\mathrm{CD}$ continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 15.0 seconds from the start?

A) $1.8 \mathrm{~m} / \mathrm{s}^{2}$
B) $0.5 \mathrm{~m} / \mathrm{s}^{2}$
C) $2.6 \mathrm{~m} / \mathrm{s}^{2}$
D) $1.0 \mathrm{~m} / \mathrm{s}^{2}$
E) $2.0 \mathrm{~m} / \mathrm{s}^{2}$

Question 29

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ 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 $4.00 \mathrm{~cm}$ from the center at the time 2.00 seconds from the start?

A) $0.100 \mathrm{~m} / \mathrm{s}^{2}$
B) $0.450 \mathrm{~m} / \mathrm{s}^{2}$
C) $0.314 \mathrm{~m} / \mathrm{s}^{2}$
D) $0.165 \mathrm{~m} / \mathrm{s}^{2}$
E) $0.215 \mathrm{~m} / \mathrm{s}^{2}$

Question 30

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ 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 $4.00 \mathrm{~cm}$ from the center at the time 10.0 seconds from the start?

A) $0.65 \mathrm{~m} / \mathrm{s}^{2}$
B) $1.25 \mathrm{~m} / \mathrm{s}^{2}$
C) $1.00 \mathrm{~m} / \mathrm{s}^{2}$
D) $1.37 \mathrm{~m} / \mathrm{s}^{2}$
E) $1.86 \mathrm{~m} / \mathrm{s}^{2}$

Question 31

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ 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 $4.00 \mathrm{~cm}$ from the center at the time 30.0 seconds from the start?

A) $0.0324 \mathrm{~m} / \mathrm{s}^{2}$
B) $0.0444 \mathrm{~m} / \mathrm{s}^{2}$
C) $0.0650 \mathrm{~m} / \mathrm{s}^{2}$
D) $0.0522 \mathrm{~m} / \mathrm{s}^{2}$
E) $0.0243 \mathrm{~m} / \mathrm{s}^{2}$

Question 32

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

A) $0.800 \mathrm{~m} / \mathrm{s}^{2}$ .
B) $0.656 \mathrm{~m} / \mathrm{s}^{2}$ .
C) $0.100 \mathrm{~m} / \mathrm{s}^{2}$ .
D) $0.980 \mathrm{~m} / \mathrm{s}^{2}$ .
E) $1.220 \mathrm{~m} / \mathrm{s}^{2}$ .

Question 33

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

A) $2.50 \mathrm{~m} / \mathrm{s}^{2}$ .
B) $0.980 \mathrm{~m} / \mathrm{s}^{2}$ .
C) $0.450 \mathrm{~m} / \mathrm{s}^{2}$ .
D) $1.25 \mathrm{~m} / \mathrm{s}^{2}$ .
E) $2.03 \mathrm{~m} / \mathrm{s}^{2}$ .

Question 34

A CD has a diameter of $12.0 \mathrm{~cm}$ and is rotating at an angular velocity of $10.0 \mathrm{rad} / \mathrm{sec}$ . If the $\mathrm{CD}$ has a constant angular acceleration of $-0.5 \mathrm{rad} / \mathrm{sec}^{2}$ , then the angular velocity of the $\mathrm{CD}$ after $3.0 \mathrm{sec}$ is

A) $6.2 \mathrm{rad} / \mathrm{s}$ .
B) $9.8 \mathrm{rad} / \mathrm{s}$ .
C) $8.5 \mathrm{rad} / \mathrm{s}$ .
D) $7.9 \mathrm{rad} / \mathrm{s}$ .
E) $5.7 \mathrm{rad} / \mathrm{s}$ .

Question 35

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

A) $1.58 \mathrm{~m} / \mathrm{s}^{2}$ .
B) $0.950 \mathrm{~m} / \mathrm{s}^{2}$ .
C) $1.25 \mathrm{~m} / \mathrm{s}^{2}$ .
D) $1.08 \mathrm{~m} / \mathrm{s}^{2}$ .
E) $1.83 \mathrm{~m} / \mathrm{s}^{2}$ .

Question 36

A 4,000 kg satellite is traveling in a circular orbit $200 \mathrm{~km}$ 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? $\left(M_{E}=5.98 \times 10^{24} \mathrm{~kg}, R_{E}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

A) $2.64 \mathrm{~m} / \mathrm{s}^{2}$
B) $4.90 \mathrm{~m} / \mathrm{s}^{2}$
C) $0.00 \mathrm{~m} / \mathrm{s}^{2}$
D) $1.62 \mathrm{~m} / \mathrm{s}^{2}$
E) $9.24 \mathrm{~m} / \mathrm{s}^{2}$

Question 37

A 4,000 kg satellite is traveling in a circular orbit $200 \mathrm{~km}$ 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? $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

A) $8.90 \mathrm{~m} / \mathrm{s}^{2}$
B) $7.95 \mathrm{~m} / \mathrm{s}^{2}$
C) $9.80 \mathrm{~m} / \mathrm{s}^{2}$
D) $9.24 \mathrm{~m} / \mathrm{s}^{2}$
E) $8.62 \mathrm{~m} / \mathrm{s}^{2}$

Question 38

A boy on a bicycle rides in a circle of radius $r_{0}$ at speed $v_{0}$ . If the boy rides at the same radius $r_{0}$ , by what approximate factor must he change his speed in order to triple his radial acceleration?

A) 9.0
B) 3.0
C) 0.33
D) 1.7
E) 0.58
F) 0.11

Question 39

A boy on a bicycle rides in a circle of radius $r_{0}$ at speed $v_{0}$ . If the boy now rides at a radius equal to half the initial radius $r_{\mathrm{o}}$ , by what approximate factor must he change his speed in order to have the same radial acceleration?

A) 0.25
B) 2
C) 0.71
D) 4
E) 0.5
F) 1.4

Question 40

Two planets travel in circular orbits about a star at radii of $r_{a}=2 R$ and $r_{b}=R$ , respectively. What is the ratio of their periods $\mathrm{T}_{\mathrm{a}} / \mathrm{T}_{\mathrm{b}}$ ?

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

Question 41

The Crab Pulsar is a neutron star, rotating with a period of about $33.085 \mathrm{~ms}$ . It is estimated to have an equatorial radius of $15 \mathrm{~km}$ , about average for a neutron star. The pulsar is slowing in its rotation so that it is expected to come to rest $9.5 \times 1010 \mathrm{~s}$ 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) $3.2 \times 10^{-10} \mathrm{~m} / \mathrm{s}^{2}$
B) $2.0 \times 10^{-9} \mathrm{~m} / \mathrm{s}^{2}$
C) $4.8 \times 10^{-6} \mathrm{~m} / \mathrm{s}^{2}$
D) $3.0 \times 10^{-5} \mathrm{~m} / \mathrm{s}^{2}$
E) $7.6 \times 10^{-7} \mathrm{~m} / \mathrm{s}^{2}$

Question 42

The Crab Pulsar is a neutron star, rotating with a period of about $33.085 \mathrm{~ms}$ . It is estimated to have an equatorial radius of $15 \mathrm{~km}$ , about average for a neutron star. The pulsar is slowing in its rotation so that it is expected to come to rest $9.5 \times 10^{10} \mathrm{~s}$ in the future. What is the magnitude of the average angular acceleration in this situation?

A) $3.2 \times 10^{-10} \mathrm{rad} / \mathrm{s}^{2}$
B) $2.0 \times 10^{-9} \mathrm{rad} / \mathrm{s}^{2}$
C) $3.0 \times 10^{-5} \mathrm{rad} / \mathrm{s}^{2}$
D) $7.6 \times 10^{-7} \mathrm{rad} / \mathrm{s}^{2}$
E) $4.8 \times 10^{-6} \mathrm{rad} / \mathrm{s}^{2}$

Question 43

At what distance from the center of the Earth would one's weight be one third of that recorded on the Earth's surface? Let the Earth's radius be $\mathrm{R}$ .

A) $1.7 \mathrm{R}$
B) $0.4 \mathrm{R}$
C) $1.4 \mathrm{R}$
D) $0.5 \mathrm{R}$
E) 3R
F) $\mathrm{R}$