Deck 9: Circular Motion

Question 1

The figure represents the velocity and the acceleration of a particle moving clockwise in a circle of radius 25.0 cm.At a certain instant of time,the magnitude of its acceleration,a = is 16.0 m/s² and it makes an angle $\theta$ = 20 ^$\circ$ with position vector as shown in the figure.At this instant,find the speed,v = of the particle.

A)4.01 m/s
B)3.29 m/s
C)2.12 m/s
D)1.94 m/s
E)0.235 m/s

Answer 1

1.94 m/s

Question 2

A roller coaster has a loop of radius 16.0 m.What does the linear speed of the roller coaster car have to be at the top of the loop for the passengers to feel weightless?

A)2.50 m/s
B)3.75 m/s
C)7.0 m/s
D)12.5 m/s
E)15.5 m/s

Answer 2

12.5 m/s

Question 3

A centrifuge in a medical laboratory is to be operated at an angular speed of 3,600 rpm (revolutions per minute).When switched on,it rotates 72.0 times before reaching the prescribed angular speed.Find the constant angular acceleration of the centrifuge while it speeds up.

A)40.0 $\pi$ rad/s²
B)50.0 $\pi$ rad/s²
C)60.0 $\pi$ rad/s²
D)70.0 $\pi$ rad/s²
E)80.0 $\pi$ rad/s²

Answer 3

50.0 $\pi$ rad/s²

Question 4

A centrifuge in a medical laboratory is to be operated at an angular speed of 3,600 rpm (revolutions per minute).If the centrifuge starts from rest and the angular acceleration is 80.0 $\pi$ rad/s²,how many revolutions does the centrifuge make as it speeds up to its operating angular speed?

A)14
B)40
C)23
D)45
E)52

Question 5

A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is kept constant and the speed is doubled

A)the centripetal acceleration remains the same.
B)the centripetal acceleration increases by a factor of 2.
C)the centripetal acceleration decreases by a factor of 2.
D)the centripetal acceleration increases by a factor of 4.
E)the centripetal acceleration decreases by a factor of 4.

Question 6

A sports utility vehicle has tires which are 110 cm in diameter.If the wheel is rotated through 30 revolutions,how far forward does a point on the tire travel?

A)54.0 m
B)86.2 m
C)90.3 m
D)104 m

Question 7

A clothes dryer is spinning at 75 rpm.A student opens its door and it comes to rest after rotating through four revolutions.Assume constant acceleration.What was the magnitude of the dryer's angular acceleration?

A)1.23 rad/s²
B)2.45 rad/s²
C)703 rad/s²
D)1410 rad/s²

Question 8

A bicycle has a wheel of radius of 14.0 inches.What is the angular speed of the wheels when the bicycle has a forward speed of 8.0 m/s?

A)12.3 rad/s
B)19.4 rad/s
C)22.5 rad/s
D)32.1 rad/s
E)45.2 rad/s

Question 9

Two hikers begin at the same initial location and walk around a circular lake in opposite directions.One walks twice as fast as the other.The circumference of the lake is L.How far does the faster hiker walk before the two hikers meet at the same final location?

A)L/3
B)L/2
C)2L/3
D)3L/4

Question 10

The angular speed of the minute hand of a clock is _______.

A)
B)
C)
D)
E)

Question 11

A plastic disk of radius 10 cm is spinning at 120 rpm.What is the magnitude of the centripetal acceleration of the outer rim of the disk?

A)15.8 m/s²
B)1440 m/s²
C)1580 m/s²
D)144 km/s²

Question 12

A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is doubled and the linear speed is kept constant,

A)the centripetal acceleration remains the same.
B)the centripetal acceleration increases by a factor of 2.
C)the centripetal acceleration decreases by a factor of 2.
D)the centripetal acceleration increases by a factor of 4.
E)the centripetal acceleration decreases by a factor of 4.

Question 13

A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is doubled and the angular speed is kept constant,

A)the centripetal acceleration remains the same.
B)the centripetal acceleration increases by a factor of 2.
C)the centripetal acceleration decreases by a factor of 2.
D)the centripetal acceleration increases by a factor of 4.
E)the centripetal acceleration decreases by a factor of 4.

Question 14

A centrifuge in a medical laboratory rotates at an angular speed of 5,400 rpm (revolutions per minute).When switched off,it rotates 100.0 times before coming to rest.Find the magnitude of the constant angular acceleration of the centrifuge while it slows down to a stop.

A)65.0 $\pi$ rad/s²
B)60.0 $\pi$ rad/s²
C)81.0 $\pi$ rad/s²
D)76.0 $\pi$ rad/s²
E)0

Question 15

A sports utility vehicle has tires which are 110 cm in diameter.The tires rotate with a constant angular speed.A point on the tire that is 0.30 m from the center has a tangential speed of 2.0 m/s.What is the tangential speed of a point on the rim of the tire?

A)0.687 m/s
B)1.57 m/s
C)2.33 m/s
D)3.67 m/s
E)4.87 m/s

Question 16

An object moves around a circle and its linear speed is always increasing.Which statement is always true?

A)Its linear velocity is perpendicular to its tangential acceleration.
B)The magnitude of its tangential acceleration is greater than the magnitude of its centripetal acceleration.
C)Its tangential and centripetal accelerations are both zero.
D)Its tangential and centripetal accelerations are perpendicular.

Question 17

The angular speed of the second hand of a clock is _______.

A)
B)
C)
D)
E)

Question 18

Two hikers begin on opposite sides of a circular lake and walk around the lake in the same direction.One walks three times as fast as the other.The circumference of the lake is L.How far does the faster hiker walk before catching up to the slower one?

A)L/3
B)L/2
C)3L/4
D)L

Question 19

A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is doubled and the angular speed is held constant,the linear speed will

A)remain the same.
B)increase by a factor of 2.
C)decrease by a factor of 2.
D)increase by a factor of 4.
E)decrease by a factor of 4.

Question 20

A ball attached to the end of a string is swung around in a circular path of radius r.If the radius is doubled and the linear speed is held constant,the angular speed will

A)remain the same.
B)increase by a factor of 2.
C)decrease by a factor of 2.
D)increase by a factor of 4.
E)decrease by a factor of 4.

Question 21

The angular acceleration versus time for an object undergoing circular motion is shown in the figure below.If the object started from rest at t = 0 s,the net angular displacement of the object at t = t_f is

A)in the clockwise direction.
B)in the counter-clockwise direction.
C)zero.
D)The displacement cannot be determined.

Question 22

A rock moves in uniform circular motion attached to a string.At point X the string is cut with a very sharp blade and the rock is no longer attached to the string.In what direction will the rock travel?

A)in toward the center (a)
B)in a curved line,away from the circle (b)
C)in a straight line (c)
D)away from the center (d)
E)None are correct.

Question 23

A ball attached to a string moves in a horizontal circle of radius 1 m.It makes one revolution in 4 seconds.The magnitude of its acceleration is

A)2.5 m/s².
B)3.9 m/s².
C)6.4 m/s².
D)9.8 m/s².
E)12.4 m/s².

Question 24

A point on Earth's surface in the northern hemisphere is moving eastward at 1300 km/h.What is the latitude of this point? (The radius of the earth is 6370 km)

A)45^o north
B)39^o north
C)30^o north
D)51^o north
E)43^o north

Question 25

A 1-m long pendulum with a mass of 5 kg moves at a velocity of 3 m/s at the bottom of its swing.What it the tension in the string at this point?

A)45 N
B)94 N
C)49 N
D)73 N
E)67 N

Question 26

An old music record rotates with 33.3 revolutions per minute.Its angular speed is

A)0.555 rad/s.
B)2.5 rad/s.
C)3.49 rad/s.
D)5.38 rad/s.
E)9.8 rad/s.

Question 27

The maximum speed a driver travel on the Daytona Speedway (bank angle )without using friction between his tires and the road to make the turn is 45 m/s.What is the radius of the turn?

A)301 m
B)401 m
C)344 m
D)241 m

Question 28

The figure represents the velocity and the acceleration of a particle moving clockwise in a circle of radius 25.0 cm.At a certain instant of time,the magnitude of its acceleration,a = is 16.0 m/s² and it makes an angle $\theta$ = 20 ^$\circ$ with position vector as shown in the figure.At this instant,what is the magnitude of the angular acceleration of the particle?

A)3.75 rad/s²
B)1.37 rad/s²
C)60.1 rad/s²
D)21.9 rad/s²
E)1.46 rad/s²

Question 29

The angular acceleration versus time for an object undergoing circular motion is shown in the figure below.If the object started from rest at t = 0 s,the net angular velocity of the object at t = t_f is

A)in the clockwise direction.
B)in the counter-clockwise direction.
C)zero.
D)The angular velocity cannot be determined.

Question 30

A racing motorcycle accelerates at a constant rate from zero to 280 km/h in 39 seconds.If the outer diameter of the motorcycle's wheels is 64 cm and they turn without slipping,the angular acceleration of each wheel is

A)5.73 rad/s².
B)11.5 rad/s².
C)3.12 rad/s².
D)22.4 rad/s².
E)6.23 rad/s².

Question 31

The angular velocity versus time for an object undergoing circular motion is shown in the figure.If the object started from rest at t = 0 s,the net angular displacement of the object at t = t_f is

A)in the clockwise direction.
B)in the counter-clockwise direction.
C)zero.
D)The displacement cannot be determined.

Question 32

The maximum speed a driver can travel on the banked curve on the Daytona Speedway is 45 m/s without using friction between his tires and the road to make the turn.The radius of the turn is 301m.What is the angle of the bank relative to the horizontal?

A)47^o
B)43^o
C)34^o
D)31^o

Question 33

A centrifuge in a medical laboratory rotates from rest to an angular speed of 3,800 rpm (revolutions per minute)while making 86.0 complete rotations.Find the time required to reach maximum speed,assuming uniform acceleration.

A)0.0423 s
B)1.36 s
C)2.72 s
D)3.14 s

Question 34

What speed can a driver travel on the Daytona Speedway (bank angle )without using friction between his tires and the road to make the turn? The radius of the turn is 301m.

A)13 m/s
B)39 m/s
C)42 m/s
D)50 m/s

Question 35

You are riding as a passenger in a car,and you round a corner,and you are pushed against the car door.Which of the following are most accurate?

A)A force pushes you outward against the car door.
B)You are traveling in a straight line while the car turns about you.
C)The car door exerts a normal force on you.
D)You are exerting a fictional force on the car door.
E)None are correct.

Question 36

A turntable is initially at rest.It starts rotating with a constant maximum angular acceleration for a period of 5 seconds.It then starts to slow down with an angular acceleration of -1 rad/s² for another 5 seconds.At the end of the 10 second period the turntable has undergone 20 rotations.What is the maximum angular acceleration the turntable reaches?

A)-1 rad/s²
B)2 rad/s²
C)1 rad/s²
D)-3.68 rad/s²
E)3.68 rad/s²

Question 37

A ceiling fan is rotating in counter-clockwise direction (looking up from the ground)but it is slowing down.What direction are and ?

A)Option A
B)Option B
C)Option C
D)Option D
E)Option E

Question 38

A flywheel with a 1 m diameter is initially at rest.Its angular acceleration versus time is given in the graph below.What is the angular separation between the initial and the final positions of a fixed point on the rim of the flywheel 8 seconds after the wheel starts rotating?

A)7.27 rad clockwise
B)7.27 rad counterclockwise
C)2.72 rad counterclockwise
D)2.72 rad clockwise
E)None are correct.

Question 39

Calgary,Canada is at a latitude of 51.0 degrees north.How fast is Calgary moving eastward as the Earth rotates? (The radius of the earth is 6370 km)

A)0 km/h
B)1050 km/h
C)1300 km/h
D)1520 km/h
E)1670 km/h

Question 40

Calgary,Canada is at a latitude of 51.0 degrees north.If one were to travel due south on the Earth's surface from Calgary,what distance would one have to cover to reach the equator.(The radius of the earth is 6370 km)

A)3310 km
B)4340 km
C)5490 km
D)5670 km
E)10,020 km

Question 41

A 45-kg woman is riding a Ferris wheel of radius 15 m at a constant speed.The speed of the Ferris wheel that would make her weightless at the top is

A)12.1 m/s.
B)9.8 m/s.
C)7.5 m/s.
D)3.2 m/s.
E)1.9 m/s.

Question 42

A CD-ROM starts from rest and undergoes uniform angular acceleration until it reaches 26,000 rpm in 0.25 s.What is its angular acceleration?

A)1.1 * 10⁴ rad/s²
B)5.4 * 10³ rad/s²
C)1.0 * 10⁵ rad/s²
D)6.5 * 10³ rad/s²

Question 43

How far does a person in Dubuque,IA (latitude 42.5 ^$\circ$ )move in the 7.50 hours she sleeps? The radius of the Earth is 6378 km.

A)4230 km
B)4620 km
C)9230 km
D)8460 km
E)12,500 km

Question 44

The surface of the exit road is horizontal,not banked.(See figure.)If the static friction between the tires and the surface of the road is µs = 0.688 and the maximum speed with which the car can exit the highway safely without sliding is 25.2 m/s,what is the radius of curvature of a highway exit ,r?

A)157 m
B)64.7 m
C)94.1 m
D)207 m
E)85.6 m

Question 45

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height),and its speed is v = 5.54 m/s,calculate the direction of the total force acting on the mass.(as measured from a line drawn from m to the center of the circular path)

A)23.7^o clockwise
B)23.7^o counterclockwise
C)66.3^o clockwise
D)66.3^o counterclockwise
E)0.00^o

Question 46

An orbital space station generates "artificial" gravity by spinning.Consider a 100-kg person standing against the outside wall of a doughnut shaped space station with an outer diameter of 2.0 km.What is the period of rotation for the space station such that the space station exerts a force on the person equal to the weight of the person on the surface of the Earth?

A)4.8 s
B)31 s
C)63 s
D)90 s
E)640 s

Question 47

A 2.0-m long string is tied to a 3.0-kg rock and the rock is twirled around in a circle at a constant speed.The speed of the rock is such that the string makes an angle of 45 degrees with the horizontal.How long does it take the rock to complete one full circle?

A)1.3 s
B)1.9 s
C)2.4 s
D)2.8 s
E)4.4 s

Question 48

A 45-kg woman is riding a Ferris wheel of radius 15 m at a constant speed.The angular speed of the Ferris wheel that would make her weightless at the top is

A)0.81 rad/s
B)0.50 rad/s
C)0.10 rad/s
D)0.65 rad/s
E)0.213 rad/s

Question 49

A car with a mass of 1200 kg goes over a hill at a constant speed.The top of the hill can be approximated as an arc length of a circle with a radius of curvature of 210 m.What minimum speed must the car have as it passes over the top of the hill in order to become airborn?

A)9.8 m/s
B)11 m/s
C)37 m/s
D)45 m/s
E)56 m/s

Question 50

The radius of curvature of a highway exit is r = 68.5 m.The surface of the exit road is horizontal,not banked.(See figure.)If the static friction between the tires and the surface of the road is µs = 0.688,then what is the maximum speed at which the car can exit the highway safely without sliding? (in m/s)

A)1.57 * 10¹
B)1.84 * 10¹
C)2.15 * 10¹
D)2.52 * 10¹
E)2.94 * 10¹

Question 51

A CD-ROM starts from rest and undergoes uniform angular acceleration until it reaches 26,000 rpm in 0.25 s.Through what angle does it rotate during this time?

A)54 rad
B)85 rad
C)340 rad
D)680 rad

Question 52

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height),and its speed is v = 5.54 m/s,calculate the magnitude of the total force acting on the mass.(in N)

A)3.64
B)5.28
C)7.65
D)1.11 * 10¹
E)1.61 * 10¹

Question 53

A car drives along a country road at a constant speed of 26 m/s.When it encounters a hill,its tires just barely leave the pavement as the car passes over the top of the hill.What is the radius of curvature of the hill?

A)69 m
B)81 m
C)250 m
D)Information about the mass of the car is needed.

Question 54

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height),and its speed is v = 5.54 m/s.Determine the tension in the rope.(in N)

A)1.47 * 10¹
B)1.67 * 10¹
C)1.88 * 10¹
D)2.13 * 10¹
E)2.40 * 10¹

Question 55

A 2.0-m long string is tied to a 3.0-kg rock and the rock is twirled around in a circle at a constant speed.The speed of the rock is such that the string makes an angle of 45 degrees with the horizontal.What is the speed of the rock?

A)2.8 m/s
B)4.0 m/s
C)3.7 m/s
D)4.4 m/s
E)5.0 m/s

Question 56

A child's top is spinning at a rate of 7.00 rev/s.It takes 30.0 seconds for the top to slow to a rate of 2.00 rev/s.Assuming a constant angular acceleration,what is the magnitude of the angular acceleration of the top?

A)0.070 rad/s²
B)0.167 rad/s²
C)0.233 rad/s²
D)1.05 rad/s²
E)1.47 rad/s²

Question 57

Suppose the people standing at rest with respect to the Earth on the Earth's equator are weightless.The radius of the earth is 6.37 * 10⁶ m.The length of the day under this condition would be

A)21 hours.
B)6 hours.
C)2.1 hours.
D)84.4 min.
E)41.5 min.

Question 58

A CD-ROM starts from rest and undergoes uniform angular acceleration until it reaches 26,000 rpm in 0.25 s.If its radius is 0.061 m,how far does a point on its edge travel during this time?

A)3.3 m
B)5.2 m
C)21 m
D)41 m

Question 59

The wheel of a racing car is rotating at 200 rpm at a given instant of time.In the next minute it makes 100 revolutions.The angular acceleration of the wheel is

A)-4.9 rad/s².
B)-2.5 rad/s².
C)-1.5 rad/s².
D)-0.50 rad/s².
E)-0.35 rad/s².

Question 60

The surface of the exit road is horizontal,not banked.(See figure.)If the radius of curvature of a highway exit is 82.5 m and the maximum speed with which the car can exit the highway safely without sliding is 25.2 m/s,what is the coefficient of static friction between the tires and the surface of the road?

A)0.69
B)0.85
C)0.78
D)0.56
E)0.72

Question 61

The moon Demos takes 30 hours 26 minutes to complete one orbit around Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,what is the radius of Demos' orbit around Mars?

A)4.08 * 10⁶ m
B)2.56 * 10⁵ m
C)8.69 * 10⁶ m
D)1.47 * 10⁸ m
E)2.35 * 10⁷ m

Question 62

A flatbed truck goes around a curve of radius R with speed V.There is a box on the truck of M kg mass.Which statement is correct concerning the net horizontal force on the box,if the box does not slide?

A)It is MV²/R outward from the center of the curve.
B)It is zero.
C)It is MV²/R inward towards the center of the curve.
D)It is MgR outward from the center of the curve.
E)It is MgR inward towards the center of the curve.

Question 63

A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L.The mass is pulled back,raised and released.If the tension in the string at the bottom of the swing is 2mg,how high was the the mass raised above the bottom of the swing?

A)0.33 L
B)0.25 L
C)0.10 L
D)0.50 L
E)0.67 L

Question 64

Two masses are attached to a 1-meter rope as shown such that half of the rope hangs vertically below the frictionless table.m₁ (= 2 kg)is set into circular motion with speed 3.0 m/s.What is the value of m₂ if m₂ is to remain stationary?

A)5.2 kg
B)4.6 kg
C)3.7 kg
D)2.5 kg
E)2.0 kg

Question 65

Somewhere on the surface of the Earth a yo-yo with m = 0.050 kg is swung in a vertical circle with radius r = 0.40 m.Find the tension on the string at the top if the speed at that point is v = 2.0 m/s.

A)3.0 N
B)27.0 N
C)81.0 N
D)0.333 N
E)0.0095 N

Question 66

A toy train moves with uniform speed on a circular track.Which of the following statements is true?

A)The angular acceleration is always positive.
B)The angular acceleration is always negative.
C)The angular acceleration can either be positive or negative,depending if the train runs clockwise or counter-clockwise.
D)The centripetal acceleration is 0.
E)The centripetal acceleration does not change in magnitude.

Question 67

A small object with a mass of m = 658 g is whirled at the end of a rope in a vertical circle with a radius of r = 137 cm.When it is at the location shown,(mid-height),and its speed is v = 5.54 m/s,calculate the magnitude of the total force acting on the mass.(in N)

A)4.91 * 10¹
B)5.82 * 10¹
C)9.81
D)2.22 * 10¹
E)2.45 * 10¹

Question 68

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's centripetal acceleration,if it makes one revolution every 90 min? (The radius of Earth is approximately 6400 km.)

A)1.12 m/s²
B)2.69 m/s²
C)5.20 m/s²
D)9.34 m/s²
E)9.81 m/s²

Question 69

A spy satellite is in circular orbit around the Earth at an altitude of 500 km above ground.What is the satellite's orbital speed,if it makes one revolution every 90 min? (You might want to know that the radius of the Earth is approximately 6400 km).

A)1 km/s
B)2 km/s
C)4 km/s
D)8 km/s
E)16 km/s

Question 70

A wheel of radius 4 m is spinning with a constant angular velocity of 2 rad/s.What is the centripetal acceleration of a point on the wheel's rim?

A)2 m/s²
B)4 m/s²
C)8 m/s²
D)16 m/s²
E)32 m/s²

Question 71

The moon Demos is 23,500 km from Mars and orbits once every 30 hours 26 minutes.Assuming that it orbits in a circular path,what is its average speed?

A)0 m/s
B)215 m/s
C)732 m/s
D)1348 m/s
E)53,210 m/s

Question 72

Two masses are attached to a 1-meter rope as shown such that part of the rope hangs vertically below the frictionless table.m₁ (= 2 kg)is set into circular motion with speed 3.0 m/s.What is the length of rope hanging vertically below the table if tension in the rope if m₂ (= 5 kg)is to remain stationary?

A)0.18 m
B)0.60 m
C)0.82 m
D)0.71 m
E)0.29 m

Question 73

A runner is running on a circular track,which is 200 m in circumference.Find the magnitude of his acceleration when he is running at a constant speed of 10.8 m/s.

A)108 m/s²
B)10.8 m/s²
C)18.5 m/s²
D)3.66 m/s²
E)200 m/s²

Question 74

Two masses are attached to a 1-meter rope as shown such that one quarter of the rope hangs vertically below the frictionless table.m₁ (= 2 kg)is set into circular motion with speed 3.0 m/s.What is the tension in the rope if m₂ is to remain stationary?

A)36 N
B)18 N
C)28 N
D)14 N
E)24 N

Question 75

The moon Demos is 23,500 km from Mars.Assuming it orbits in a circular path and its average speed is 1348 m/s,how much time does it take Demos to complete one orbit?

A)1.10 * 10⁵ s
B)4.89 * 10³ s
C)7.11 * 10⁵ s
D)9.54 * 10⁵ s
E)1.74 * 10⁴ s

Question 76

On a curved roadway of radius 100 m,the suggested speed limit is 35 mph (approximately 16 m/s).What must the coefficient of friction be between a car's tires and the road for the car to safely negotiate the curve at the posted speed?

A)0.72
B)0.51
C)0.26
D)0.40
E)0.13

Question 77

An amusement park ride has a diameter of 16 meters and revolves at 15 rpm (revolutions per minute).How fast is a rider moving if she sits at the outermost part of the ride?

A)29.4 m/s
B)1.07 m/s
C)225 m/s
D)9.81 m/s
E)12.6 m/s

Question 78

It takes a runner 10 seconds to run the curve (100 meter arc length,semicircle)in a race.The centripetal acceleration acting on her is

A)1.00 m/s².
B)1.57 m/s².
C)1.92 m/s².
D)3.14 m/s².
E)3.59 m/s².