Physics Ch 5
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
.314 s
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
.52 radians
A boy on a bicycle rides in a circle of radius ro at speed vo. If the boy now rides at a radius equal to half the initial radius ro, by what approximate factor must he change his speed in order to have the same radial acceleration?
.71
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
** .250 s
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?
** .84
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
** 100 N
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
** 23.6 m
A car travels on a road that, if viewed from the side, has a semicircular bump. When at the top of the bump, the occupants of the car feel as though they weigh half their normal weight. What is the speed of the car if the radius of the semicircle is 120 m?
** 34.3 m/s
An object makes three complete rotations in the clockwise direction. What is its angular displacement?
-6π
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
.314 s
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
.79 radians
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
.800 m/s^2
If the frequency is 50 Hz, then what are the period and angular speed?
0.02 s, 100π rad/s
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? (ME = 5.98 × 1024 kg, RE = 6.37 × 106 m, G = 6.67 × 10−11 N·m2/kg2)
0.277 N
Rank the following angles with the smallest angle at the top and the largest at the bottom.
1 rad pi/2 rad 180 degrees
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?
1.0 m/s ^2
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?
1.0 m/s ^2
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?
1.0 m/s ^2
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
1.2 m/s
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
1.26 m/s
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.
1.4R
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
1.5 m/s
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
1.51 m/s
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 R.
1.7 R
Four acrobats ride unicycles from one side of the circus tent to the other. The wheels of the unicycles all roll without slipping. Each acrobat travels the same horizontal distance. Rank them according to speed, with the slowest at the top.
10 10 10 30 20 20 10 50
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
10.4 m/s horizontal
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
10.8 km.
Your car's wheels are 65.0 cm in diameter, and the wheels are spinning at an angular velocity of 102 rad/s. How fast is your car moving (assume no slippage)?
119.34 km/h
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?
12.4 m/s
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?
17.0 m/s
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
2.09 m
Two planets travel in circular orbits about a star at radii of ra = 2R and rb = R, respectively. What is the ratio of their periods Ta/Tb?
2.8
A carnival ride spins its riders in a circle of radius 20 m. The angular speed of the ride is 10 rad/s. What is the magnitude of radial acceleration of the riders?
2000 m/s^2
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
23.8 km
What is the period of a geostationary satellite that orbits the Earth?
24 hours
A wheel of radius 30.0 cm is rotating at a rate of 3.10 revolutions every 0.0810 s. Through what angle does the wheel rotate in 1.00 s?
240.42 rad
The four identical wheels of a car all roll without slipping. They all have a radius of 20 cm, and they all spin about their axles at 20 rad/s. How much time does it take the car to travel 100 m along a straight, level road?
25 s
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
250 N
An object makes one complete rotation. What is the magnitude of its angular displacement?
2π
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?
3.0 × 10−5 m/s2
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?
3.13 m/s
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
3.18 Hz
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
3.18 Hz
A ball rolls on the ground at a speed of 3.0 m/s without slipping. If the radius of the ball is 10 cm, what is the angular speed of the ball?
30 rad/s
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
32.2 m/s
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
37.7 rad/s.
A wheel of radius 30.0 cm is rotating at a rate of 3.10 revolutions every 0.0810 s. What is the wheel's frequency of rotation?
38.27 Hz
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
4.8 m
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
40 N
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?
438 N
A small object of mass 0.500 kg is attached by a 0.860 m-long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 8.80 m/s. What is the tension in the cord?
45.02 N
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
48.1 N toward the center
Rank the following situations according to the magnitude of the car's tangential acceleration, with the largest magnitude at the top and the smallest at the bottom.
50 1 50 2 20 1 20 2
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
50.1 N
Rank the following situations according to the magnitude of the car's tangential acceleration, with the largest magnitude at the top and the smallest at the bottom.
500 0.0 1100 0.04 200 0.01 100 0.01
A curve in a stretch of highway has radius 512 m. The road is unbanked. The coefficient of static friction between the tires and road is 0.700. What is the maximum safe speed that a car can travel around the curve without skidding?
59.26 m/s
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
6.0 rad/s
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?
65
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?
65 m
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 (ME = 5.98 × 1024 kg, RE = 6.37 × 106 m, G = 6.67 × 10−11 N·m2/kg2)
7,460 m/s
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
7.07 m/s
A wheel of radius 30.0 cm is rotating at a rate of 3.10 revolutions every 0.0810 s. What is the linear speed of a point on the wheel's rim?
7212 cm/s
A car travels on a road that, if viewed from the side, has a semicircular dip. When at the bottom of the dip, the occupants of the car feel as though they weigh twice their normal weight. What is the radius of the semicircle if the speed of the car is 27 m/s?
74 m
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
8.5 rad/sec
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? (ME = 5.98 × 1024 kg, RE = 6.37 × 106 m, G = 6.67 × 10−11 N·m2/kg2)
9.24 m/s ^2
A small object of mass 0.500 kg is attached by a 0.860 m-long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 8.80 m/s. What is the magnitude of the radial acceleration of the object?
90.5 m/s^2
Ice skaters have locked arms and are rotating in a line about a fixed vertical axis of rotation. Which skater moves with the largest angular speed?
All skaters have the same angular speed.
Rank the following sets of data according to the magnitude of the average angular velocity, with the largest magnitude at the top and the smallest at the bottom.
A wheel spins around completely 5 times in 10 seconds A wheel rotates 10 radiant in 5 secondsA wheel rotates 5 radians in 10 seconds
What is the definition of average angular velocity?
Angular displacement divided by time interval
Select all of the following quantities that determine the speed of a planet that is in a stable, circular orbit around a star.
Distance from the star to the center of gravity of the planet Mass of the star
According to Kepler's first law, what are the shapes of the orbits of all of the planets?
Elliptical
A car travels on a banked circular curve at constant speed. All four of the car's tires roll without slipping. The car moves at just the right speed so that the frictional force is zero. Ignore air resistance. Select all of the following forces that act on the car.
Gravitational force Normal force
A conical pendulum is shown in the figure. The mass m moves in a circle of radius r in the horizontal plane. The dashed line is vertical. The string sweeps out the surface of a right circular cone, with the apex of the cone at the top where the string is attached to the ceiling. Which of the following is the radial component of the net force?
Horizontal component of the tension
A tether ball is attached to the top of a vertical pole by a string. The tether ball moves in a circle in the horizontal plane. The string sweeps out the surface of a right circular cone, with the apex of the cone at the top where the string is attached to the top of the pole. Which of the following causes the tether ball to move with uniform circular motion?
Horizontal component of the tension in the string
What is the advantage to banking the plane when making a turn?
It creates a horizontal component to the lift.
How does a centrifuge work?
It creates artificial gravity. It uses the object's inertia to move it outward.
A wheel is spinning around its center at 30 rad/s and a point on its outer edge is moving at 6 m/s. If the angular speed of the wheel is increased, then what will happen to the linear speed of the point on its outer edge?
It will increase.
According to Kepler's third law, if the average distance from a planet to the Sun increased by a factor of four, then what would happen to the planet's orbital period?
It would increase by a factor of eight.
If both the orbital period and the average distance to the Sun are known for one of the planets, then what can be determined from Kepler's third law?
Mass of the Sun
Rank the following planets in terms of their orbital speed, with the largest orbital speed at the top and the smallest at the bottom.
Planet orbiting a star at a distance of 1x10^11m, and the mass of the star is equal to the mass of the sun Planet orbiting a star at a distance of 1x10^11m, and the mass of the star is equal to half the mass of the sun Planet orbiting a start at a distance of 3x10^11m, and the mass of the star is equal to the mass of the sun Planet orbiting a star at a distance of 3x10^11m, and the mass of the star is equal to half the mass of the sun
For an object in circular motion, which of the following causes the direction of the velocity of the object to change?
Radial acceleration
What is the direction of the radial acceleration?
Radially inward
The arc length s, subtended by an angle θ in a circle of radius r, is given by s = rθ. In which units must θ be measured?
Radians
Select all of the following that could be units of angular speed.
Radians per second Cycles per second
A car travels on an unbanked circular curve at constant speed. All four of the car's tires roll without slipping. Ignore air resistance. Select all of the following forces that act on the car.
Static frictional force Gravitational force Normal force
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?
T
For an object in circular motion, which of the following causes the magnitude of the velocity of the object to change?
Tangential acceleration
Pick the answer that applies to uniform circular motion.
The acceleration is always perpendicular to the motion.
What is the definition of average angular acceleration?
The change in the angular velocity divided by the time interval
Select all of the following statements that are true regarding ring-shaped space stations that rotate in order to create artificial gravity.
The direction of the apparent gravitational field is radially outward. The floors on the rooms are farthest away from the axis of rotation.
Select all of the following effects that are caused by nonzero radial acceleration.
The direction of the object's velocity changes. The object moves around a circle.
For this question, assume that the Earth is a rotating rigid body. Select all of the following that are true.
The distance between any two points on the surface of the Earth always remains the same. Every point on the surface of the Earth moves in a circular path.
A car travels on an unbanked circular curve at constant speed. All four of the car's tires roll without slipping. Select all of the following statements that are true.
The force of friction acts toward the center of the circle. The force of static friction acts on the tires.
An airplane flies in the air around a horizontal circle at constant speed. Which statement is true?
The horizontal component of the lift force acts toward the center of the circle.
A car travels on a banked circular curve at constant speed. All four of the car's tires roll without slipping. The car moves at just the right speed so that the frictional force is zero. Which statement is true?
The horizontal component of the normal force acts toward the center of the circle.
Rank the apparent weight of a person standing on the surface of the Earth at the following locations with the largest apparent weight at the top and the smallest at the bottom. Assume that the Earth is a perfect sphere.
The north geographic... The Arctic Circle The equator
Which of the following would lead to apparent weightlessness?
The only force acting on an object is gravity.
Select all of the following statements that are true of the period.
The period can be measured in seconds. The period is equal to 1 divided by the frequency.
If we assume the Earth to be perfectly spherical, choose the reasons the apparent weight of an object at rest at the equator is less than the apparent weight of an object at the North Pole.
The radial acceleration is greater.
Select all of the following that are true of instantaneous angular acceleration.
The rate of change of an object's angular velocity is its instantaneous angular acceleration.α av = Δω/Δt
Ice skaters have locked arms and are rotating in a line about a fixed central point. Which skater moves with the largest linear speed?
The skater farthest from the axis of rotation
A curve in a stretch of highway has radius 512 m. The road is unbanked. The coefficient of static friction between the tires and road is 0.700. When the car enters the curve at a speed greater than the maximum safe speed (speed at which the car won't skid), which of the following statements are correct?
The static frictional force is not large enough to keep the car in a circular path. The car skids toward the outside of the curve.
Select all of the following equations that are true for apparent weightlessness.
W = mg a = g
Select all of the following that are true for a rigid body.
When a rigid body rotates, every point of the body moves in a circular path. The distance between any two points of the body remains the same when the body translates and/or rotates.
An object moving in a circle at a constant speed is
accelerating toward the center of the circle.
For a satellite to be geostationary, what must be the shape of its orbit?
circular
For circular motion to be called uniform circular motion, the speed must remain ______ throughout
constant
A space station is rotating at 30 rad/min, which will create a radial acceleration with a magnitude of g. A delegation of aliens wishes to visit the station. To make them feel welcome, the crew of the station wishes to increase the magnitude of the radial acceleration to approximate the alien's home world's magnitude of acceleration due to gravity. Should they increase or decrease the rotational speed?
increase
When a girl swings in a tire swing, the tangential acceleration in the rope
is the greatest at the highest point of the motion.
What is the amount of time it takes for an object moving in a circle to make one rotation?
period
According to Kepler's third law of planetary motion, the ______ of the period of a planet is proportional to the cube of the average orbital ________
square radius
Match each linear variable with its rotational counterpart.
x --> θ v --> w a --> a
Match each kinematic equation for linear motion with constant linear acceleration with its rotational counterpart for rotational motion with constant angular acceleration.
xf = xi + vit + 12 at2 --> θf = θi + ωit + 12 αt2vf = vi + at--> ωf = ωi + αtvf2 = vi2 + 2a(xf - xi) --> ωf2 = ωi2 + 2α(θf - θi)
