Deck 7: Rotational Motion and Gravitation

Question 1

An automobile accelerates from zero to 36.72 m/s in 6.80 s.The wheels have a diameter of 0.450 m.What is the average angular acceleration of each wheel?

A)12.0 rad/s²
B)24.0 rad/s²
C)33.6 rad/s²
D)21.9 rad/s²
E)18.0 rad/s²

Answer 1

24.0 rad/s²

Question 2

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

A)rev/min²,m/s
B)deg/hour,rev/minute
C)rad/s²,deg/hour
D)rad/s,rad/s²

Answer 2

rad/s²,deg/hour

Question 3

2 600 rev/min is equivalent to which of the following?

A)2 600 rad/s
B)43.3 rad/s
C)272 rad/s
D)60.0 rad/s

Answer 3

272 rad/s

Question 4

Suppose a car has a 100 000-mile 10-year warranty on its wheels and axles.How may turns will the wheels of 0.70-m diameter make if both the mileage and time warranties run out simultaneously and what will be the average angular velocities of the wheel? Assume that a mile = 1.6 × 10³ m and that a year is 3.16 × 10⁷ s.

A)7.3E+7,14 rad/s
B)2.3E+8,1.4 rad/s
C)3.5E+8,1.4 rad/s
D)7.3E+7,1.4 rad/s
E)2.3E+8,14​ rad/s

Question 5

A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 5.0-s interval?

A)12.5 rad
B)25 rad
C)2.0 rad
D)0.50 rad

Question 6

A ceiling fan is turned on and reaches an angular speed of 132 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 40 s.The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?

A)6.6
B)6.4
C)−0.15
D)−2.0

Question 7

What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

A)7.3 × 10−⁵ rad/s
B)3.6 × 10−⁵ rad/s
C)6.3 × 10−⁵ rad/s
D)3.1 × 10−⁵ rad/s

Question 8

A Ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad.What is its average angular acceleration?

A)9.3 rad/s²
B)0.37 rad/s²
C)2.6 rad/s²
D)0.39 rad/s²

Question 9

A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?

A)3.2 rad/s
B)26 rad/s
C)52 rad/s
D)81 rad/s

Question 10

Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?

A)0.25T
B)0.50T
C)0.67T
D)0.71T

Question 11

A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 10.4-s interval at a rate of 0.040 0 rad/s².What angular displacement does the Ferris wheel undergo in this 10.4-s interval?

A)7.4 rad
B)0.21 rad
C)2.2 rad
D)0.0019 rad

Question 12

A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 7.0-s interval at a rate of 0.040 rad/s².What is its angular speed after this 7.0-s interval?

A)0.20 rad/s
B)0.30 rad/s
C)0.46 rad/s
D)0.78 rad/s

Question 13

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate.Point 1 on the disk is located at a distance r₁ from the center of the disk and point 2 on the disk is located at a distance r₂ from the center of the disk.If r₂ = 2r₁,which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below,all values occurring at the same time.​

A)ω₂/ω₁
B)α₂/α₁
C)a_c2/ac₁
D)All the ratios are 1 so none is larger.

Question 14

Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?

A)0.50T
B)0.67T
C)0.71T
D)all of the above

Question 15

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20.0 s.It is then turned off and coasts to a stop in 40.0 s.In the 60.0 s of rotation,through how many revolutions did the fan turn?

A)251
B)377
C)126
D)188

Question 16

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is its angular speed at the instant it goes through an angular displacement of 7.00 rad?

A)280 rad/s
B)0.175 rad/s
C)0.592 rad/s
D)880 rad/s

Question 17

A 0.12-m-radius grinding wheel takes 6.0 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration?

A)5.6 rad/s²
B)0.22 rad/s²
C)1.5 rad/s²
D)0.080 rad/s²

Question 18

Suppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s after 36.0 seconds have elapsed.How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 36.0-second interval?

A)0.556 s
B)22.2 s
C)18.0 s
D)56.5 s

Question 19

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is the time interval required for it to reach a 6.50-rad displacement after starting from rest?

A)3.61 s
B)260 s
C)0.163 s
D)22.8 s

Question 20

A spool of thread has an average radius of 1.00 cm.If the spool contains 47.5 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

A)15.1
B)756
C)149
D)7.56

Question 21

A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s².What is the angular speed of the wheel?

A)1.0 rad/s
B)2.0 rad/s
C)3.2 rad/s
D)4.0 rad/s

Question 22

The Earth is 93.0 million miles from the Sun and its period of revolution is 1 year = 3.15 × 10⁷ s.What is the acceleration of the Earth in its orbit about the Sun?

A)18.6 mi/s²
B)9.30 × 10−³ mi/s²
C)13.6 × 10−⁶ mi/s²
D)3.70 × 10−⁶ mi/s²

Question 23

A point on the rim of a 0.15-m-radius rotating disk has a centripetal acceleration of 5.0 m/s².What is the angular speed of a point 0.075 m from the center of the disk?

A)0.89 rad/s
B)1.6 rad/s
C)3.2 rad/s
D)5.8 rad/s

Question 24

The distance from the center of a Ferris wheel to a passenger seat is 12 m.What centripetal acceleration does a passenger experience when the wheel's angular speed is 0.50 rad/s?

A)17 m/s²
B)9.0 m/s²
C)3.0 m/s²
D)6.0 m/s²

Question 25

Consider a point on a bicycle wheel as the wheel turns about a fixed axis,neither speeding up nor slowing down.Compare the linear and angular velocities of the point.

A)Both are constant.
B)Only the angular velocity is constant.
C)Only the linear velocity is constant.
D)Neither is constant.

Question 26

A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 5.0 m/s.What is the tangential speed of a point 0.20 m from the center of the same wheel?

A)1.0 m/s
B)0.50 m/s
C)3.3 m/s
D)17 m/s

Question 27

A 0.150-m-radius grinding wheel starts at rest and develops an angular speed of 12.00 rad/s in 7.80 s.What is the average tangential acceleration of a point on the wheel's edge?

A)0.231 m/s²
B)1.54 m/s²
C)10.3 m/s²
D)14.0 m/s²

Question 28

A cylindrical space colony 8.00 km in diameter and 30.0 km long has been proposed as living quarters for future space explorers.Such a habitat would have cities,land,and lakes on the inside surface and air and clouds in the center.All this would be held in place by the rotation of the cylinder about the long axis.How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder?

A)0.049 rad/s
B)0.035 rad/s
C)0.0025 rad/s
D)0.15 rad/s

Question 29

Consider a point on a bicycle wheel as the wheel turns about a fixed axis,neither speeding up nor slowing down.Compare the linear and angular accelerations of the point.

A)Both are zero.
B)Only the angular acceleration is zero.
C)Only the linear acceleration is zero.
D)Neither is zero.

Question 30

When a point on the rim of a 0.30-m-radius wheel experiences a centripetal acceleration of 4.0 m/s²,what tangential acceleration does that point experience?

A)1.2 m/s²
B)2.0 m/s²
C)4.0 m/s²
D)Cannot determine with the information given.

Question 31

A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m.How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?

A)3.0 rev/s
B)1.5 rev/s
C)0.48 rev/s
D)0.24 rev/s

Question 32

A point on the rim of a 0.25-m-radius fan blade has centripetal acceleration of 0.20 m/s².Find the centripetal acceleration of a point 0.05 m from the center of the same wheel.

A)0.01 m/s²
B)0.02 m/s²
C)0.04 m/s²
D)0.08 m/s²

Question 33

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s².What is the centripetal acceleration of a point on the outer edge of the tire after 5.0 s?

A)300 m/s²
B)33 m/s²
C)30 m/s²
D)3.0 m/s²

Question 34

A ventilation fan has blades 0.25 m long rotating at 20 rpm.What is the centripetal acceleration of a point on the outer tip of a blade?

A)1.1 m/s²
B)0.87 m/s²
C)0.55 m/s²
D)0.23 m/s²

Question 35

An airplane in a wide sweeping "outside" loop can create zero gees inside the aircraft cabin.What must be the radius of curvature of the flight path for an aircraft moving at 150 m/s to create a condition of "weightlessness" inside the aircraft?

A)1 150 m
B)1 800 m
C)2 300 m
D)3 600 m

Question 36

Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis.Compare the linear and angular displacement of the point.

A)Both are zero.
B)Only the angular displacement is zero.
C)Only the linear displacement is zero.
D)Neither is zero.

Question 37

A 0.150-m-radius grinding wheel,starting at rest,develops an angular speed of 12.0 rad/s in a time interval of 4.00 s.What is the centripetal acceleration of a point 0.100 m from the center when the wheel is moving at an angular speed of 12.0 rad/s?

A)0.450 m/s²
B)7.20 m/s²
C)14.4 m/s²
D)28.8 m/s²

Question 38

A 0.40-kg mass,attached to the end of a 0.75-m string,is whirled around in a circular horizontal path.If the maximum tension that the string can withstand is 450 N,then what maximum speed can the mass have if the string is not to break?

A)370 m/s
B)22 m/s
C)19 m/s
D)29 m/s

Question 39

Calculate the linear speed due to the Earth's rotation for a person at the equator of the Earth.The radius of the Earth is 6.40 × 10⁶ m.

A)74.0 m/s
B)233 m/s
C)465 m/s
D)73.0 m/s

Question 40

The end of the cutting cord on a gas-powered weed cutter is 0.21 m in length.If the motor rotates at the rate of 20 rev/s,what is the tangential speed of the end of the cord?

A)13 m/s
B)4.2 m/s
C)26 m/s
D)2.7 m/s

Question 41

A wheel is rotated about a horizontal axle at a constant angular speed.Next it is rotated in the opposite direction with the same angular speed.The acceleration at a point on the top of the wheel in the second case as compared to the acceleration in the first case:

A)is in the same direction.
B)is in the opposite direction.
C)is upward.
D)is tangential to the wheel.

Question 42

At what speed will a car round a 52.0-m-radius curve,banked at a 40.0° angle,if no friction is required between the road and tires to prevent the car from slipping? (g = 9.80 m/s²)

A)18.1 m/s
B)22.6 m/s
C)20.7 m/s
D)43.6 m/s

Question 43

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s² over a 5.0-s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 5.0-s interval?

A)33 m/s²
B)6.7 m/s²
C)0.60 m/s²
D)0.30 m/s²

Question 44

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 60.0° N latitude.The radius of the Earth is 6.40 × 10⁶ m.

A)403 m/s
B)233 m/s
C)37.0 m/s
D)74.1 m/s

Question 45

In order to train for a high-g environment,an astronaut is placed in a centrifuge of radius several meters and rotated in a horizontal circle at constant speed.In this situation,in which direction is the net force on the astronaut?

A)The net force is down since gravity cannot be turned off.
B)The net force is horizontal toward the center of the circle.
C)The net force is between horizontal toward the center of the circle and straight up,the angle depending on the speed and the radius involved.
D)The net force is zero since the astronaut is moving at constant speed and thus the force has no direction.

Question 46

For a point on a spinning disc in uniform circular motion,which of the following is not constant?

A)Its angular speed.
B)Its angular acceleration.
C)Its centripetal acceleration.
D)The magnitude of its total acceleration.

Question 47

A car is going around a racetrack at constant speed.The curves around the track have different radii.In which turn is the magnitude of the car's acceleration the greatest?

A)It is the greatest in the turn with the greatest radius.
B)It is the greatest in the turn with the smallest radius.
C)The acceleration is zero everywhere because of the constant speed.
D)More information is needed to determine the answer.

Question 48

A ventilation fan has blades 0.25 m in radius rotating at 20 rpm.What is the tangential speed of each blade tip?

A)0.020 m/s
B)0.52 m/s
C)5.0 m/s
D)20 m/s

Question 49

At what angle (relative to the horizontal)should a curve 52.0 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 11.6 m/s? (g = 9.80 m/s²)

A)0.264°
B)1.30°
C)14.8°
D)2.59°

Question 50

Two points on a merry-go-round are located at distances from the center r₁ and r₂,where r₁ < r₂.While the merry-go-round is in the process of speeding up to operational speed,which of the following equations involving magnitudes of angular speed,angular acceleration,and tangential speed for these points is incorrect?

A)ω₁ = ω₂
B)α₁ = α₂
C)vt₁ = vt₂
D)All of the equations are correct.

Question 51

What angular speed (in revolutions/second)is needed for a centrifuge to produce an acceleration of 1 000 g at a radius arm of 15.0 cm?

A)40.7 rev/s
B)75.4 rev/s
C)81.4 rev/s
D)151 rev/s

Question 52

What centripetal force does an 80.0-kg passenger experience when seated 10.0 m from the center of a Ferris wheel whose angular speed is 0.500 rad/s?

A)2.00 N
B)24.5 N
C)400 N
D)200 N

Question 53

A roller coaster,loaded with passengers,has a mass of 2 000 kg;the radius of curvature of the track at the bottom point of the dip is 24 m.If the vehicle has a speed of 18 m/s at this point,what force is exerted on the vehicle by the track? (g = 9.8 m/s²)

A)4.7E+4 N
B)2.7E+4 N
C)2.0E+4 N
D)7.4E+3 N

Question 54

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1 200g at a radius arm of 15.0 cm?

A)0.0280 rev/s
B)44.6 rev/s
C)14.2 rev/s
D)6.68 rev/s

Question 55

A 0.30-kg rock is swung in a circular path and in a vertical plane on a 0.25-m-length string.At the top of the path,the angular speed is 12.0 rad/s.What is the tension in the string at that point?

A)7.9 N
B)16 N
C)18 N
D)83 N

Question 56

A 0.650-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string.If the angular speed at the bottom is 8.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?

A)27.2 N
B)20.8 N
C)14.4 N
D)6.37 N

Question 57

​Pierre performs a maneuver with his yo-yo called "around the world",where he swings the yo-yo in a vertical circle.When the yo-yo is at its highest point,which forces provide the centripetal acceleration?

A)​friction
B)​gravity
C)​normal force
D)​tension
E)​Two of the above choices are correct.

Question 58

Consider a child who is swinging.As she reaches the lowest point in her swing:

A)the tension in the rope is equal to her weight.
B)the tension in the rope is equal to her mass times her acceleration.
C)her acceleration is downward at 9.8 m/s².
D)none of the above.

Question 59

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12.0 m/s.What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

A)0.024
B)0.23
C)0.28
D)1.2

Question 60

Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed.The direction for the acceleration for this point at that moment is:

A)upward.
B)down toward the ground.
C)forward.
D)at that moment the acceleration is zero.

Question 61

Suppose the gravitational potential energy for a mass at an altitude of one Earth radius is PE₁ and at two Earth radii is PE₂.How do the absolute values of these potential energies compare?

A)|PE₁| = 2|PE₂|
B)|PE₁| = 4|PE₂|
C)|PE₁| < 2|PE₂|
D)|PE₁| > 2|PE₂| but is not equal to 4|PE₂|

Question 62

A satellite is in a circular orbit about the Earth at a distance of d = 5 times the Earth's radius above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 × 10⁶ m. )

A)4.2E+2 m/s
B)1.3E+5 m/s
C)3.2E+3 m/s
D)3.3E+6 m/s

Question 63

Two objects are in circular orbits of different radii around the Sun.Which object has the highest orbital speed?

A)The one closest to the Sun.
B)The one farthest from the Sun.
C)Once in orbit around the Sun,all objects have the same orbital speed regardless of distance from the Sun.It is the greater radius and greater resulting circumference that causes the object farther from the Sun to take longer to complete an orbit.
D)This cannot be found without knowing the relative masses of the objects.

Question 64

If the mass of Venus is 0.786 times that of Earth,and its radius is 0.950 that of Earth,estimate the gravitational acceleration g at the surface of Venus.(g_earth = 9.80 m/s²)

A)7.31 m/s²
B)3.73 m/s²
C)8.27 m/s²
D)8.53 m/s²

Question 65

An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location?

A)nearest the Earth
B)farthest from the Earth
C)between Earth and Moon
D)between Earth and Sun

Question 66

Doubling the mean distance from the Sun results in changing the orbital period of revolution by what factor?

A)2^1/2
B)2
C)2^3/2
D)2²

Question 67

A double-star system with each star having the mass of the Sun has an orbital period of 1 year.A second double star system,also with each star having the mass of the Sun,has an orbital period of 8 years.If the separation of the stars in the first system is d and the orbits in both cases are circular,what is the separation of the stars in the second system?

A)0.5d
B)2d
C)4d
D)8d

Question 68

A planet has mass M = 8.00 × 10²³ kg.At what distance will the centripetal acceleration of an orbiting space station be equal to the gravitational acceleration on Earth's surface? (G = 6.67 × 10^-11 m³·kg^-1·s^-1)

A)2.33 × 10⁶ m
B)5.44 × 1012 m
C)5.23 × 10¹⁴ m
D)1.18 × 1035 m

Question 69

For any object orbiting the Sun,Kepler's law may be written T² = kr³.If T is measured in years and r in units of the Earth's distance from the Sun,then k = 1.What,therefore,is the time (in years)for Mars to orbit the Sun if its mean radius from the Sun is 1.5 times the Earth's distance from the Sun?

A)1.8 years
B)2.8 years
C)3.4 years
D)4.2 years

Question 70

An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 2.0 N.What is the object's mass? (g at the surface of the Earth is 9.80 m/s²)

A)0.22 kg
B)18 kg
C)1.8 kg
D)0.46 kg

Question 71

The acceleration due to gravity at the surface of Planet X is 10 m/s².What is the acceleration due to gravity at an altitude of 3 000 km above the surface of this planet?

A)10 m/s²
B)8.0 m/s²
C)4.4 m/s²
D)More information is needed.

Question 72

An asteroid is in orbit at 4 times the Earth's distance from the Sun.What is its period of revolution?

A)one fourth year
B)4 years
C)8 years
D)16 years

Question 73

Two satellites are monitored as they orbit the Earth;satellite X is eight times as far from the Earth's center as is satellite Y.From Kepler's third law one may conclude that the period or revolution of X is what factor times that of Y?

A)
B)
C)
D)

Question 74

An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the Sun.What is its linear speed when it is at its greatest distance from the Sun,a distance 2d?

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

Question 75

A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon.If the value of g on Io is 2.0 m/s²,estimate the speed with which the liquid sulfur left the volcano.

A)260 m/s
B)530 m/s
C)790 m/s
D)970 m/s

Question 76

An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4 000 miles).At this location,the acceleration due to gravity is what factor times the value of g at the Earth's surface?

A)There is no acceleration since the satellite is in orbit.
B)2
C)1/2
D)1/4

Question 77

A satellite is in a circular orbit about the Earth at a distance of two Earth radii above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 × 10⁶ m,and G = 6.67 × 10−¹¹ N × m²/kg². )

A)2 800 m/s
B)4 600 m/s
C)5 600 m/s
D)17 000 m/s

Question 78

An object of mass 0.50 kg weighs 2.0 N when it is 1.0 × 10⁶ m above the surface of Planet X.The radius of the planet is 4.0 × 10⁶ m.What free-fall acceleration will the 0.50-kg object experience when at the surface of Planet X?

A)4.8 m/s²
B)2.0 m/s²
C)4.0 m/s²
D)6.3 m/s²

Question 79

If a planet has a radius 16.0% greater than that of the Earth but has the same mass as the Earth,what is the acceleration due to gravity at its surface?

A)8.45 m/s²
B)1.57 m/s²
C)10.0 m/s²
D)7.28 m/s²

Question 80

An object of mass m is on the surface of the Earth.The distance to the Sun and the Moon are d_S and d_M,and the masses of the Sun and Moon are M_S and M_M.What is the ratio of the gravitational force from the Sun to that of the Moon on the object?

A)M_SM_M /d_Sd_M
B)M_SM_M /d²_Sd²_M
C)M_Sd²_M /M_Md²_M
D)M_Md²_S /M_Sd²_M