A bicycle racer is going downhill at 14.0 m/s when, to his horror, one of his 2.14-kg wheels comes off when he is 67.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0 cm in diameter and neglect the small mass of the spokes. 1)How fast is the wheel moving when it reaches the foot of the hill if it rolled without slipping all the way down? Express your answer in meters per second.   2)How much total kinetic energy does the wheel have when it reaches the bottom of the hill? Express your answer in joules.

A 1.0-kg mass hangs on a rope wrapped around a frictionless disk pulley of mass 5 kg and radius 0.5 m. What is the acceleration of the mass? (The moment of inertia of the pulley is 1/2MR2.)

An electric grinder is switched on at t = 0, accelerates uniformly for 15 s to its operating angular speed of 22 rad/s. The wheel then turns at constant angular speed for 35 s and is switched off, slowing uniformly at 3.5 rad/s² until it stops. From the time it is switched off, how long does the grinder take to stop turning? t = S Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary.

A rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per second

A solid ball (sphere) of mass 1 kg and radius 0.3 m is held at rest at the top of a ramp. There is enough friction so that the ball will roll down the ramp without slipping. The top of the ramp is 10 meters above the ground.What will the speed be of the ball just before it hits the bottom of the ramp?

An electric fan is turned off, and its angular velocity decreases uniformly from 450 rev/min to 220 rev/min in a time interval of length 4.50s.  a) Find the angular acceleration α in revolutions per second per second.  b) Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A.  c) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A?

Consider a phonograph with a diameter of 0.6 m and a rotational speed of 33 RPM. Answer the following questions. What is its radius in m?What is its rotational speed in rad/s?What is the tangential speed on the phonograph's outer edge in m/s?What is the tangential speed at the center of the phonograph in m/s?What is the tangential speed halfway out to the edge of the phonograph?

A 8.6-cm-diameter, 389 g sphere is released from rest at the top of a 3.2-m-long, 25° incline. It rolls, without slipping, to the bottom. (a) What is the sphere's angular velocity at the bottom of the incline?

The tires of a car make 85 revolutions as the car reduces its speed uniformly from 87.0 km/hkm/h to 58.0 km/hkm/h. The tires have a diameter of 0.82 mm. What was the angular acceleration of the tires? If the car continues to decelerate at this rate, how much more time is required for it to stop? If the car continues to decelerate at this rate, how far does it go? Find the total distance.

A turntable plays a vinyl with a mass of 0.186 kg and with a diameter of 0.089 meters. The vinyl rotates about an axis through its center with 0.698 J of kinetic energy. What is the speed (in m/s) of a point on the rim? The moment of inertia of the vinyl is I = (1/2)MR2