AP Physics

A car traveling down the road at 25.0 m/s has a wheel spinning at 45.0 rad/s. A deer jumps in front of the car causing the driver to slam on the brakes and slow to 10.0 rad/s in 1.75 s. What is the angular acceleration of the car?

-20.0 rad/s^2

A boy takes a toy top and pulls on a string to make the top spin. The top can be considered a solid disk (I=½MR2) and has a mass of 0.100kg and a radius of 0.0200m. The top starts from rest and ends up spinning at 15.0rev/s after 0.800s. What is the torque applied to the top?

0.00236 Nm

A grinding wheel is rotating with an angular velocity of 251 radians per second, find the period of one revolution.

0.0250 s

A 135 g meter stick rotates with an angular velocity of 3.50 rad/s about an axis perpendicular to the stick and passing through the middle of the stick. What is the magnitude of the angular momentum of the meter stick. A very good approximation of the moment of the meter stick is that of a long thin rod, I=mL^2/12.

0.0394 kg∙m^2/s

A 45.0 kg child runs at 5.00 m/s, tangentially, up to a 200. kg stationary merry-go-round and hops onto the outer edge of the merry-go-round. The radius of the merry-go-round is 2.40 m. Assume that merry-go-round is free to rotate on a frictionless axel and that its moment of inertia is 1/2MR2. Treat the child as a point mass with moment of inertia MR2. Find the angular velocity of the merry-go-round after the child hopped on.

0.647 rad/s

The moment of inertia of a uniform rod (about its center) is given by I=(ML^2)/12. What is the kinetic energy of a 1.20m rod with mass 0.90 kg rotating about its center at 3.6 rad/s.

0.70 J

Suppose three planets, each with a mass of 2.0x10^25 kg, are arranged in an equilateral triangle at a distance of 4.0x10^12 m on each leg. Calculate the force between m1 and m2.

1.67x10^15 N

The an object that has rotated through an angular measure of 115° has an angular displacement equal to

2.01 rad

The gravitational force between two objects of mass M and 2M respectfully, is measured to be F when the two are placed a distance R from each other. If the M mass is replaced by a mass of 2M, what is the new force between the two masses?

2F

A merry-go-round with a radius of 1.5 m is spinning at 2.0 rad/s when a young girl pushes on it for 5.0 s applying an acceleration of 3.0 rad/s^2. What is the angular displacement of the merry-go-round during this time?

48 rad

A car traveling down the road at 25.0 m/s has a wheel spinning at 45.0 rad/s. A deer jumps in front of the car causing the driver to slam on the brakes and slow to 10.0 rad/s in 1.75 s. What is the angular displacement of the car assuming that the wheels slow without slipping?

48.1 rad

A road bike has tires that have a diameter of 0.800m and is rolling down the road at 20.0m/s. What is the angular velocity of the bike tire?

50.0 rad/s

A planet orbits the sun in an elliptical path, with the furthest distance from the sun (aphelion) of 70x10^9 m and the closest distance (perihelion) of 46 x 10^9 m. If the planet is traveling 39 km/s at aphelion, how fast is it traveling at perihelion?

59 km/s

A constant horizontal force of magnitude F=9.0 N is applied to the axle of a solid disk as shown. The disk has a mass of 5.0 kg and a diameter of 0.20 m. If the disk starts from rest and rolls without slipping, what is the linear speed of the center of the disk after it has moved a distance of 15 m? The moment of inertia of a solid disk is ½mr^2.

6.0 m/s

A 50 N·m torque acts on a wheel of moment of inertia 150 kg·m^2. If the wheel starts from rest, how long will it take the wheel to make one revolution?

6.1 s

Find the time required for a turntable to accelerate at a constant rate from rest to an angular velocity of 477 rev/min if it experiences a constant acceleration of 7.94 rad/s^2.

6.30 s

A hollow cylinder with thin walls, of radius 3.05 m, has a mass of 73 kg. Since all of the mass is concentrated at the radius of the cylinder, its moment of inertia is is mR^2. How much work is required, without the hoop slipping, to bring it from rest to an angular velocity of of 0.305 m/s?

6.79 J

The earth takes 8.62 x 10^4 s to complete one rotation about its axis of rotation. Find the angular velocity of the earth.

7.29 x 10^-5 rad/s

A car traveling down the road at 25.0 m/s has a wheel spinning at 45.0 rad/s. A deer jumps in front of the car causing the driver to slam on the brakes and slow to 10.0 rad/s in 1.75 s. How many revolutions does the wheel pass through as it slows down?

7.66 rev

A prize wheel is spinning in a vertical circle when an acceleration of 2.0 rad/s^2 is applied to the edge of the wheel as it spins through 5.0 rad. If the final velocity of the wheel was measured to be 9.0 rad/s, what was the initial velocity of the wheel?

7.8 rad/s

A window washer with a mass of 75.0kg stands 4.00 m from the left side of a 125kg platform that is 5.00m long. The platform is uniform so that the center of mass is in the middle of the platform. What is the tension on the rope that supports the platform on the left?

760 N

Suppose three planets, each with a mass of 2.0x10^25 kg, are arranged in an equilateral triangle at a distance of 4.0x10^12 m on each leg. Describe the free body diagram for m1 at the origin.

A force F12 (force on planet 1 due to 2) pointing to the upper right along the leg of the equilateral triangle

The same torque is applied to two objects. The first is a distance R from the pivot point and at a right angle to the torque arm. The second is at a distance 2R from the pivot and also at right angles to the torque arm. If the first had a force F applied to it, what was the value of the second force?

F/2

Find an expression for the radius of a circular orbit, R, for a satellite of mass m, that orbits a planet of mass, M, with a velocity v.

R = GM/v^2

Above the surface of the earth, the acceleration due to gravity

varies inversely with the square of the distance from the center of Earth.

A circular platform of radius 4.0 m is initially spinning with an angular velocity of 8.0 rad/s. The platform accelerates for 2.0 s while passing through a displacement of 10. rad. What is the angular acceleration of the system.

-3.0 rad/s^2

A road bike has tires that have a diameter of 0.800m and is rolling down the road at 20.0m/s. What is the angular acceleration of the tire as it comes to a stop?

-5.00rad/s^2

A solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy? (I=½MR^2)

0.092 J

A boy takes a toy top and pulls on a string to make the top spin. The top can be considered a solid disk (I=½MR2) and has a mass of 0.100kg and a radius of 0.0200m. The top starts from rest and ends up spinning at 15.0rev/s after 0.800s. If the boy pulled 0.500m of string that from the edge of the top at a tangent to the arc of the top, what force did he apply?

0.118 N

An object that has experienced a 3.0 radian angular displacement has made how many revolutions?

0.48 rev

A 0.25 m radius grinding wheel is rotating with a constant angular speed of 2.0 rad/s. Find the tangential speed at the edge of the wheel.

0.5 m/s

A circular platform of radius 4.0 m is initially spinning with an angular velocity of 8.0 rad/s. The angular velocity is then increased to 10 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. What is the magnitude of the angular acceleration of the platform?

0.50 rad/s^2

A spherical shell of radius 0.25 m, and mass 3.8kg, is initially at rest. Assuming a constant net torque is applied to the shell, how much power is required to bring the shell up to an angular velocity of 13 rad/s in 25 s? The moment of inertia of a shell is (2/3)MR^2.

0.54 W

A 45 kg child runs at 5.5 m/s at an angle of 90° to the radius of a stationary merry-go-round and hops onto the merry go-round at the outer edge. The merry-go-round has a mass of 150 kg and a radius of 3.0m. Treat the merry-go-round as a solid disk with moment of inertia of ½ MR^2. Find the angular velocity of the merry-go-round after the child hops on.

0.69 rad /s

A meter stick is hung from the ceiling with a string attached to the center. A 3.0 kg mass is hung from the 0.10 m line on the meter stick. Where should a 5.0 kg mass be hung to balance the meter stick.

0.74 m line

A father is helping his daughter change the oil in her car. They are both applying a perpendicular force in the counterclockwise direction to a wrench to loosen the oil plug. Her force is 4.0N at 7.0cm from the plug and his is 14N 4.0cm from the plug. Find the torque applied to the oil plug.

0.84 N·m

A 45.0 kg child runs at 5.00 m/s, tangentially, up to a 200. kg stationary merry-go-round and hops onto the outer edge of the merry-go-round. The radius of the merry-go-round is 2.40 m. Assume that merry-go-round is free to rotate on a frictionless axel and that its moment of inertia is 1/2MR2. Treat the child as a point mass with moment of inertia MR2. After the merry-go-round, with the child aboard, is rotating, the child crawls half-way to the center of the merry-go-round. Find the angular velocity of the merry-go-round with the child in this new position.

0.843 rad /s

An object falling to the earth has what acceleration due to gravity when it is at a location 2R above the surface of the Earth, where R is the radius of the Earth?

1.09 m/s^2

A prize wheel is spinning in a vertical circle at 2.0 rad/s when an acceleration is applied to the wheel to increase the velocity to 6.0 rad/s. How long did this acceleration last if the displacement during this time was 5.0 rad.

1.2 s

A boy takes a toy top and pulls on a string to make the top spin. The top can be considered a solid disk (I=½MR^2) and has a mass of 0.100kg and a radius of 0.0200m. The top starts from rest and ends up spinning at 15.0rev/s after 0.800s. What is the angular acceleration of the top?

118 rad/s^2

A window washer with a mass of 75.0kg stands 4.00 m from the left side of a 125kg platform that is 5.00m long. The platform is uniform so that the center of mass is in the middle of the platform. What is the tension on rope that supports the platform on the right?

1200 N

A 0.350m radius solid cylinder is released from rest and rolls down a ramp inclined 21.0° from horizontal. The moment of inertia of a solid cylinder is ½ MR2. After the cylinder has rolled a distance of 5.00m find: the angular velocity of the cylinder

13.8 rad/s

A ball, mass m=5.0 kg, moves in a straight line at v=10 m/s as shown. At the instant shown, what is its angular momentum about the point P?

150 kg·m^2/s

A 4.0 m radius circular platform rotates with a constant angular acceleration of 20.0 rad/s^2. What is the acceleration of a point on the edge of the disk at the instant that its angular speed is 1.0 rev/s?

180 m/s^2

An ice cream machine requires a given torque to be applied to the crank. If an operator applies this torque at half the radius in the same amount of time, the operator is expending ___ times the power.

2

Given a round object (sphere, disk, hoop for example), doubling only the mass of the object changes its moment inertia by a factor of:

2

What is the force between the Earth and the moon given that the Earth has a mass of 5.98 x 10^24 kg, the moon has a mass of 7.35 x 10^22 kg and the radius of the moon's orbit is 3.85 x 10^8 m?

2 x 10^20 N

A satellite in circular orbit about the moon has an acceleration due to gravity of 0.14 m/s^2. If the acceleration due to gravity is 1.62 m/s^2 on the moon's surface, what is the height of the satellite above the surface of the moon?

2.4R

Consider two point masses spaced 1 m apart along the x axis. 2.0 kg is located at 2.0m 3.0 kg is located at 3.0m Find where along the x axis the center of mass is located.

2.6 m

Suppose three planets, each with a mass of 2.0x1025 kg, are arranged in an equilateral triangle at a distance of 4.0x1012 m on each leg. Find the magnitude and direction of the gravitational force on m1 located at the origin.

2.89x10^15 N, 29.9° above +x

A car tire rotating at 30.0 rad/s has gone through how many revolutions in 5.00 s.

23.9 rev

A road bike has tires that have a diameter of 0.800m and is rolling down the road at 20.0m/s. Seeing a stop sign the bike rider applies the breaks to bring the bike to a stop in 100.0m. What is the angular displacement of the tires as the bike comes to a stop?

250. rad

A hoop with a radius R and a mas M has a momentum of inertia I. What would be the moment of inertia of a second hoop with the same radius but twice the mass?

2I

In the diagram above the smaller circle has a diameter R and the larger a diameter 2R. If a mass M is hung from the rope on the right side, what must be the mass on the left rope for the system to be in static equilibrium?

2M

A bicycle with wheels radius r is traveling with a linear velocity v and an angular velocity w. A second bicycle has the same angular velocity but has twice the linear velocity. What is the radius of the second bicycles wheels?

2r

A prize wheel is spinning in a vertical circle when an acceleration of 2.0 rad/s^2 is applied to the edge of the wheel for 3.0 s. If the final velocity of the wheel was measured to be 9.0 rad/s, what was the initial velocity of the wheel?

3.0 rad/s

What is the radius of an orbit of a satellite that orbits Uranus once every 145 hours? The mass of Uranus is 8.69x10^25 kg.

3.42×10^8 m

A man is holding an 8.00 kg block at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is held at 30.0° below the horizontal?

37.3 N·m

Given a round object (sphere, disk, hoop for example), doubling only the radius of the object changes its moment inertia by a factor of:

4

A pebble is stuck in the treads of a truck tire of radius 0.55 m, turning at an angular speed of 8.0 rad/s as it rolls on a horizontal surface without slipping. What is the speed of the pebble relative to the road when it is at the bottom of the tire?

4.4 m/s

A circular platform of radius 2.0 m is initially spinning with an angular velocity of 8.0 rad/s. The angular velocity is then increased to 10. rad/s as the platform accelerates through 4.0 rad. Assume that the angular acceleration is constant. What is the magnitude of the angular acceleration of the platform?

4.5 rad/s^2

Find the tangential speed of ant on a turntable if the ant is 0.114 m from the axis of rotation and the turntable is rotating at 6.5 rev/sec.

4.7 m/s

A 0.350m radius solid cylinder is released from rest and rolls down a ramp inclined 21.0° from horizontal. The moment of inertia of a solid cylinder is ½ MR2. After the cylinder has rolled a distance of 5.00m find: the speed of the cylinder

4.84 m/s

A point mass, M, is rotating horizontally at the end of a string with a radius R with an angular velocity W. The string is slowly pulled in so the radius decreases to R/2. What is the angular velocity of the point mass?

4W

A solid disk of mass m and radius r undergoes an acceleration a. A second disk also with a radius r only accelerates at a/4 when the same torque is applied. What is the mass of the second disk?

4m

A solid sphere of radius R rotates about its center with an initial angular velocity, ω0. The sphere then collapses to radius R/2. What is the final angular speed of the sphere? The moment of inertia of a solid sphere is (2/5) mR^2.

4ω0

A car traveling in a straight line at 14 m/s when the driver puts on the brakes and comes to a stop in 35 m. How much time did it take for the car to come to a stop?

5.0 s

Four masses are connected by rods of negligible mass as shown. How much power is required to accelerate the system from rest to 3.25 rad/s with a constant angular acceleration in 40 s. about an axis perpendicular to the x-y plane and passing through the 3.00 kg mass. Treat each mass as a point mass with moment of inertia MR^2.

5.2 W

A massless 1.5 m rod connects 2 equal point masses, one at each end of the rod. If the kinetic energy is 36 J when rotating this system at 3 rad/s about an axis perpendicular to the rod through one end of the rod, what is the value of the moment of inertia of the system?

8 kgm^2

A string is wrapped around a pulley of radius 0.10 m and moment of inertia 0.15 kg·m^2. The string is pulled with a force of 12 N. What is the magnitude of the resulting angular acceleration of the pulley?

8.0 rad·s^2

A pebble is stuck in the treads of a truck tire of radius 0.55 m, turning at an angular speed of 8.0 rad/s as it rolls on a horizontal surface without slipping. What is the speed of the pebble relative to the road when it is at the top of the tire?

8.8 m/s

A 4.0 m radius circular platform accelerates from rest at 10.0 rad/s^2. What is the linear displacement of the edge of the circular platform after 2.0 s?

80. m

A 0.010 m radius drill bit rotates with a constant angular velocity of 5.0 rev/s. What is the linear acceleration of a point on the edge of the drill bit?

9.9 m/s^2

Given that the frequency of a rotating bicycle tire is 15 Hz, find the angular frequency.

94 rad/s

As you watch the tumbler in a clothes dryer spin clockwise at a constant speed, what is the direction of the angular velocity?

Away from you

Sitting in front of a fan on a hot summer day, the moment after you turn on the fan, what is the angular acceleration of the fan blades as they are speeding up. (fan blades rotate clockwise)

Away from you

Sitting in front of a fan on a hot summer day, you can see that the fan blade is moving clockwise. What is the direction of the fans angular displacement vector?

Away from you

Which of the satellites shown orbits the earth at the smallest speed?

C

Rank the speeds of the satellites from least to greatest.

C, B=D, A

An object with an angular velocity of 0

Could have a net torque being applied to it

An object is a distance R from the pivot point and at a right angle to the torque arm and experiences a torque T. A second object is is at a distance 2R from the pivot and also at right angles to the torque arm and experiences a torque T/2. If the first had a force F applied to it, what was the value of the second force?

F/4

A rigid body rotates with a constant angular acceleration. Which one of the following statements is true concerning the tangential acceleration of any point on the body?

It depends on the change in the angular velocity.

In the diagram above the smaller circle has a diameter R and the larger a diameter 2R. If a mass 2M is hung from the rope on the left side, what must be the mass on the right rope for the system to be in static equilibrium?

M

A point of mass M, is rotating at distance R from the center of its path with an angular velocity W. What is the angular momentum of the point?

MR^2W

A thin hoop of mass M, with a radius R, is spinning with an angular velocity W. What is the angular momentum of the hoop?

MR^2W

Satellite A is in orbit about a planet A of mass M. Satellite B is in orbit about a planet B that has twice the mass of planet A, and orbits about planet B with an orbital radius of four times that of satellite A. Compare the speed of satellite B to that of A. B has ____ the speed of A.

None of these choices is correct

Two masses one with a mass M and the other with a mass 2M are place a distance R apart from each other as indicated above. What is the center of mass of the system relative to the center of the right mass?

R/3

A merry-go-round is spinning at a constant angular velocity

The net torque on the merry-go-round must be 0

Which of the following does not represent rotational power?

The product of torque and angular velocity.

A parent and child are on a carnival ride rotating at a constant angular velocity. The parent is at the outer edge and the child is closer to the center. Who has the greater tangential acceleration?

They both have zero tangential acceleration.

Fixing the brakes on your bicycle, you have the bicycle turned upside down. To test the brakes, you spin the wheel to a high speed in a clockwise direction from your perspective. As you apply the brakes and wheel is slowing, what is the direction of the angular acceleration?

Toward you

Satellite A is in orbit about a planet. Satellite B has the same orbital radius about planet B which has one fourth the mass of planet A. Compare the period of satellite B to that of A. B has ____ the period of A.

Twice

A torque T is applied to a point mass causing it to spin around a point. If the torque is applied through a displacement θ in a time t, what is the power being applied to the point mass?

Tθ/t

A solid disk of mass m and radius r undergoes an acceleration a. What would be the acceleration of a second disk of mass m and radius 2r if the same torque were applied to it?

a/4

A DVD rotates about its center at constant uniformly increasing angular velocity. For a speck of dust at the edge of the disk which of the following is constant?

angular acceleration

An object is in rotational equilibrium only if it...

has zero angular acceleration

A person is standing at the outer edge of a circular platform, initially rotating freely at a constant angular velocity. As the person walks toward the center of the rotating platform, what happens and why? The angular velocity of the system...

increases because the moment of inertia of the system has decreased.

As a spinning star collapses into a neutron star of a smaller radius, retaining essentially all of its original mass, its angular...

momentum remains constant.

You are holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. As you start to turn left, you feel the right side of the axle

push on your right hand vertically down.

An airplane engine rotates counterclockwise when viewed by the pilot who is sitting behind the engine. When the plane turns left,

the airplane tends to dive.