Exam 9: Rotational Motion

A solid,uniform,horizontal disk with a diameter of 2.0 m and a mass of 4.0 kg freely rotates at 36 rpm about a vertical axis through its center.A small 0.50-kg stone is suddenly dropped onto the disk and sticks to the disk at a distance of 80 cm from the axis of rotation.The figure shows before and after views. (a)Before the stone fell,what was the moment of inertia of the disk about its central axis? (b)After the stone stuck,what was the moment of inertia of the system about the same axis? (c)What is the angular velocity of the disk (in rpm)after the stone fell onto the disk?

A bicycle has wheels that are 60 cm in diameter.What is the angular speed of these wheels when it is moving at 4.0 m/s?

When an old LP turntable was revolving at 33 $\frac { 1 } { 3 }$ rpm,it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a)What was the magnitude of its angular acceleration (in rad/s²)as it slowed down? (b)Through how many revolutions did it turn while stopping?

A light-weight potter's wheel,having a moment of inertia of $24 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ is spinning freely at 40.0 rpm.The potter drops a small but dense lump of clay onto the wheel,where it sticks a distance 1.2 m from the rotational axis.If the subsequent angular speed of the wheel and clay is 32 rpm,what is the mass of the clay?

When a fan is turned off,its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s.What is the magnitude of the average angular acceleration of the fan?

A pencil that is 15.7 cm long is released from a vertical position with the eraser end resting on a table.The eraser does not slip as it tips over.Treat the pencil like a uniform rod.What is the angular speed of the pencil just before it hits the table?

A mechanic is examining the wheel of a bicycle to adjust the brake.With the bicycle off the ground,he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop.If the wheel has a moment of inertia of 0.100 kg ∙ m²,and the wheel slows uniformly to a stop in 160 s,what is the magnitude of the retarding torque?

A futuristic design for a car is to have a large flywheel within the car to store kinetic energy.The flywheel is a solid uniform disk of mass 370 kg with a radius of 0.50 m,and it can rotate up to $200 \mathrm { rev } / \mathrm { s }$ Assuming all of this stored kinetic energy could be transferred to the $1500 - \mathrm { kg }$ car to change its linear speed of,find the maximum attainable speed of the car.

A solid uniform cylinder is rolling without slipping.What fraction of its kinetic energy is rotational?

The L-shaped object shown in the figure consists of three small mass objects connected by extremely light rods.Assume that the masses shown are accurate to three significant figures.How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s (a)about the x-axis,(b)about the y-axis?

A bicycle wheel has an outside diameter of 66 cm.Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m.What is the magnitude of its angular acceleration if there was no slipping?

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min.When switched off,it makes 50 complete turns at a constant angular acceleration before coming to rest. (a)What was the magnitude of the angular acceleration of the centrifuge as it slowed down? (d)How long did it take for the centrifuge to come to rest after being turned off?

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The angular velocity of the sphere at the bottom of the incline depends on

A wheel of diameter 0.70 m rolls on the floor without slipping.A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a)At what speed is the central axis of the wheel moving relative to the floor? (b)What is the angular speed of the wheel?

A uniform ball with diameter of 10 cm rolls without slipping on a horizontal tabletop.The moment of inertia of the ball about an axis through its center is 2.2 × 10^-3 kg ∙ m²,and the translational speed of its center is 0.45 m/s. (a)What is its angular speed of the ball about its center of mass? (b)What is the rotational kinetic energy of the ball? (c)What is the ball's angular momentum about its center of mass?

A solid wooden door,90 cm wide by 2.0 m tall,has a mass of 35 kg.It is open and at rest.A small 500-g ball is thrown perpendicular to the door with a speed of 20 m/s and hits the door 60 cm from the hinged side,causing it to begin turning.The ball rebounds along the same line with a speed of 16.0 m/s relative to the ground.How much mechanical energy is converted to internal energy during this collision?

The figure shows scale drawings of four objects,each of the same mass and uniform thickness,with the mass distributed uniformly.Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P? A. B. C. D.

A solid uniform 3.33-kg disk has thin string of negligible mass wrapped around its rim,with one end of the string tied to the ceiling,as shown in the figure.The disk is released from rest,and as it falls,it turns as the string unwraps.At the instant its center has fallen 2.25 m,(a)how fast is the center moving,and (b)how much rotational kinetic energy does the disk have?

A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill,starting from rest.If the angular speed of the disk is 4.27 rad/s at the bottom,how high did it start on the hill?