Exam 8: Rotational Kinematics

A bicycle wheel of radius 0.70 m is rolling without slipping on a horizontal surface with an angular speed of 2.0 rev/s when the cyclist begins to uniformly apply the brakes. The bicycle stops in 5.0 s. -How far did the bicycle travel during the 5.0 seconds of braking?

Joe is painting the floor of his basement using a paint roller. The roller has a mass of 2.4 kg and a radius of 3.8 cm. In rolling the roller across the floor, Joe applies a force F = 16 N directed at an angle of 35° as shown. Ignoring the mass of the roller handle, what is the magnitude of the angular acceleration of the roller?

What is the angular speed in rad/s of the second hand of a watch?

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 12 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. -What is the average angular speed of the grindstone?

An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 420 rev/min. If the angular acceleration is constant, how many revolutions does the propeller undergo during this time?

A top is spinning counterclockwise as shown in the figure. It is also moving to the right with a linear speed v. What is the direction of the angular velocity?

A car is moving along a horizontal road at a constant velocity that is directed 45° south of east. What is the direction of the angular velocity of the wheels of the car?

A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s². What is its angular speed after it has turned through an angle of 628 radians?

During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 0.250 rev. What is the angular acceleration of the CD?

A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 12 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 grindstone?

A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over a 3.0-s interval. What is the angular acceleration of a point on the wheel?

The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles. The actual time is 8.616 × 10⁴ s. Given this information, what is the angular speed of the Earth about its axis?

A ball attached to a string starts at rest and undergoes a constant angular acceleration as it travels in a horizontal circle of radius 0.30 m. After 0.65 sec, the angular speed of the ball is 9.7 rad/s. What is the tangential acceleration of the ball?

A spinning disc rotating at 130 rev/min slows and stops 31 s later. How many revolutions did the disc make during this time?

What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation; and the wheel is rotating at 6.53 rev/sec?

A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. What is its angular acceleration?

A sculptor is sharpening a chisel on grindstone of radius 1.0 m that is spinning with a constant angular speed of 2.0 rad/s. -What is the tangential speed of a point on the rim of the grindstone?

A circular disk of radius 0.015 m rotates with a constant angular speed of 5.0 rev/s. What is the acceleration of a point on the edge of the disk?

On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. -What is the instantaneous tangential speed of the passengers 15 s after the acceleration begins?

A wheel turns through an angle of 188 radians in 8.0 s; and its angular speed at the end of the period is 44 rad/s. If the angular acceleration is constant, what was the angular speed of the wheel at the beginning of the 8.0 s interval?