Deck 7: Rotational Motion and the Law of Gravity

Question 1

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 4.2-rad displacement after starting from rest?

A) 1.8 s
B) 2.0 s
C) 16 s
D) 18 s

Answer 1

18 s

Question 2

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-s interval?

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

Answer 2

0.78 rad/s

Question 3

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

Answer 3

0.50 T

Question 4

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) 6.28 × 10−⁵ rad/s
D) 3.14 × 10−⁵ 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 point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 4.0 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) 1.3 m/s
C) 2.7 m/s
D) 8.0 m/s

Question 7

A ceiling fan is turned on and reaches an angular speed of 120 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) 2
B) 0.5
C) −0.5
D) −2

Question 8

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad.What is its average angular acceleration?

A) 0.10 rad/s²
B) 0.05 rad/s²
C) 1.8 rad/s²
D) 0.60 rad/s²

Question 9

A spool of thread has an average radius of 1.00 cm.If the spool contains 62.8 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) 100
B) 1 000
C) 3 140
D) 62 800

Question 10

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

A) 0.02 m/s
B) 0.52 m/s
C) 5.0 m/s
D) 20 m/s

Question 11

A 0.15-m-radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s.What is the average tangential acceleration of a point on the wheel's edge?

A) 0.45 m/s²
B) 6.8 m/s²
C) 28 m/s²
D) 14 m/s²

Question 12

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

A) 2600 rad/s
B) 43.3 rad/s
C) 273 rad/s
D) 60 rad/s

Question 13

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

Question 14

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-s interval?

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

Question 15

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 16

A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 7.00-s interval at a rate of 0.040 0 rad/s².What angular displacement does the Ferris wheel undergo in this 7-s interval?

A) 4.48 rad
B) 2.50 rad
C) 3.00 rad
D) 0.500 rad

Question 17

A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration?

A) 9.6 rad/s²
B) 4.8 rad/s²
C) 1.6 rad/s²
D) 0.33 rad/s²

Question 18

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?

A) 20
B) 60
C) 0
D) 600

Question 19

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 4.2 rad?

A) 0.025 rad/s
B) 0.11 rad/s
C) 0.46 rad/s
D) 1.2 rad/s

Question 20

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 20.0 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 20.0 second interval?

A) 10.0 s
B) 12.4 s
C) 14.2 s
D) 15.0 s

Question 21

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 22

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 23

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 24

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 25

What centripetal force does an 80-kg passenger experience when seated 12 m from the center of a Ferris wheel whose angular speed is 0.50 rad/s?

A) 484 N
B) 720 N
C) 914 N
D) 240 N

Question 26

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 27

A 0.400-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) 5.60 N
B) 10.5 N
C) 16.7 N
D) 19.6 N

Question 28

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 29

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 30

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 31

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 32

The end of the cutting cord on a gas-powered weed cutter is 0.15 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) 628 m/s
B) 25 m/s
C) 19 m/s
D) 63 m/s

Question 33

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 34

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 35

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 40° N latitude.The radius of the Earth is 6.40 × 10⁶ m.

A) 299 m/s
B) 357 m/s
C) 390 m/s
D) 465 m/s

Question 36

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 37

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 38

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12 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) 0.18
B) 0.30
C) 0.28
D) 0.37

Question 39

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 40

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) 16.9 m/s²
B) 9.0 m/s²
C) 3.0 m/s²
D) 6.0 m/s²

Question 41

You are facing east looking at the clock on the wall.You see the second hand moving clockwise (of course).In what direction is the angular velocity vector for this second hand?

A) east
B) west
C) north or south,but not east or west
D) For half the rotation it is east,and for the other half of the rotation it is west.

Question 42

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 43

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.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) 48 m/s²
B) 20 m/s²
C) 16 m/s²
D) 40 m/s²

Question 44

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) 2.3 × 10⁴ N
B) 4.7 × 10⁴ N
C) 3.0 × 10⁴ N
D) 1.0 × 10⁴ N

Question 45

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.The radius of the planet is 4.0 × 10⁶ m.What free fall acceleration will the 0.50-kg object experience when transported to a distance of 2.0 × 10⁶ m from the surface of this planet?

A) 90 m/s²
B) 20 m/s²
C) 13 m/s²
D) 18 m/s²

Question 46

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 47

If a planet has 3 times the radius of the Earth,but has the same density as the Earth,what is the gravitational acceleration at the surface of the planet? (g = 9.8 m/s²)

A) 29.4 m/s²
B) 88.2 m/s²
C) 265 m/s²
D) 3.27 m/s²

Question 48

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 49

The Earth is 93 million miles (mi)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) 9.3 × 10−³ mi/s²
C) 13.6 × 10−⁶ mi/s²
D) 3.7 × 10−⁶ mi/s²

Question 50

If a planet has a radius 20% 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) 14 m/s²
B) 12 m/s²
C) 8.2 m/s²
D) 6.8 m/s²

Question 51

An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 1.00 N.What is the object's mass? (g at the surface of the Earth is 9.8 m/s²)

A) 0.102 kg
B) 0.306 kg
C) 0.92 kg
D) 1.0 kg

Question 52

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 53

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 54

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 55

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 56

At what speed will a car round a 52-m-radius curve,banked at a 45° angle,if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

A) 27 m/s
B) 17 m/s
C) 23 m/s
D) 35 m/s

Question 57

At what angle (relative to the horizontal)should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g = 9.8 m/s²)

A) 28°
B) 32°
C) 16°
D) 10°

Question 58

A cylindrical space colony 8 km in diameter and 30 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) 0.05 rad/s
B) 0.10 rad/s
C) 0.15 rad/s
D) 0.20 rad/s

Question 59

Somewhere between the Earth and the Moon is a point where the gravitational attraction of the Earth is canceled by the gravitational pull of the Moon.The mass of the Moon is 1/81 that of the Earth.How far from the center of the Earth is this point?

A) 8/9 the way to the Moon
B) 9/10 the way to the Moon
C) 3/4 the way to the Moon
D) 80/81 the way to the Moon

Question 60

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.The radius of the planet is 4.0 × 10⁶ m.What is the mass of Planet X? (G = 6.67 × 10−¹¹ N ⋅ m²/kg²)

A) 13 × 10¹⁹ kg
B) 17 × 10²² kg
C) 9.6 × 10²⁴ kg
D) 21 × 10²⁵ kg

Question 61

Which of the following best describes the property of the period of orbital revolution for an Earth satellite?

A) greater when the orbital radius is smaller
B) greater when the orbital radius is larger
C) independent of the orbital radius
D) determined mainly by the satellite's mass

Question 62

In order for a satellite to be geosynchronous,its orbit must:

A) go over the North and South Poles.
B) be over the equator.
C) be over a single longitude.
D) emit television signals.

Question 63

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 2 d?

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

Question 64

Geosynchronous satellites orbit the Earth at a distance of 42 000 km from the Earth's center.Their angular speed at this height is the same as the rotation rate of the Earth,so they appear stationary at certain locations in the sky.What is the force acting on a 1 500-kg satellite at this height?

A) 85 N
B) 333 N
C) 404 N
D) 457 N

Question 65

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) 1/2
B) 2.0
C) 4.0
D) 22.6

Question 66

According to Kepler's second law,Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse.What is at the other focus of the ellipse?

A) nothing
B) the Earth
C) The comet itself passes through the other focus.
D) The tail of the comet stays at the other ellipse.

Question 67

Of the nine known planets in our solar system,the innermost is Mercury.When compared to the other planets in the system,Mercury has the:

A) greatest centripetal acceleration.
B) greatest period of revolution.
C) smallest angular velocity.
D) smallest tangential velocity.

Question 68

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)

B)

C)

D)
but is not equal to

Question 69

The Earth's orbit is closest to the Sun in January and farthest from the Sun in July.When is the Earth moving the fastest in orbit?

A) Neither January nor July since the orbital speed of the Earth is a constant.
B) January
C) July
D) This occurs twice a year,in April and in October.

Question 70

At an altitude of 4 times the radius of the earth,the acceleration due to gravity is

A) g/2.
B) g/4.
C) g/16.
D) not given.

Question 71

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 72

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 73

If the mass of Mars is 0.107 times that of Earth,and its radius is 0.530 that of Earth,estimate the gravitational acceleration g at the surface of Mars.(g_earth = 9.80 m/s²)

A) 2.20 m/s²
B) 3.73 m/s²
C) 4.20 m/s²
D) 5.50 m/s²

Question 74

At what location does an artificial Earth satellite in elliptical orbit have its greatest speed?

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

Question 75

A satellite is in a circular orbit about the Earth at a distance of one Earth radius 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) 4 200 m/s
C) 5 600 m/s
D) 16 800 m/s

Question 76

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 77

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 78

The escape speed from the surface of the Earth is 11.2 km/s.Estimate the escape speed for a spacecraft from the surface of the Moon.The Moon has a mass 1/81 that of Earth and a radius 0.25 that of Earth.

A) 2.5 km/s
B) 4.0 km/s
C) 5.6 km/s
D) 8.7 km/s

Question 79

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 80

An asteroid has a perihelion (the orbit's closest approach to the sun)of 1.5 AU and a period of revolution of 8.0 y.What is its greatest distance from the sun (its aphelion)?

A) 8.0 AU
B) 6.5 AU
C) 4.0 AU
D) 2.5 AU