Chipola Junior College

Practice rotation problems

1. A massless turntable is used to play records . Each record is essentially a solid cylinder with a radius of 0.15 m and mass 0.1 kg. There is a constant frictional force of 0.5 N due to a wire rubbing against the record a distance of 0.05 m from the axis of rotation. Answer the following questions assuming that you apply a tangential force on the record with your finger at a distance of 0.1 m from the axis of rotation.

a) When playing, the record rotates at a frequency of 33.3 rpm. What angular velocity does this correspond to?

b) Calculate the average angular acceleration of the record if it spins from rest to its operating speed after 4 full rotations.

c) You apply a tangential force on the record with your finger at a distance of 0.1 m from the axis of rotation in order to rotate the record as described above. What must the magnitude of the force be in order for you to achieve the angular acceleration found in part b).

d) How much work does it take to bring the record from rest to it's operating speed?

2. Consider a 20 kg merry-go-round shaped like a cylinder of diameter 3 m. A metal bar sticks up on the surface of the merry-go-round at a distance of 1 m from the center so a person can apply a tangential force at this point. Ignore the effect of friction.

a) How much work must be done to get the merry-go-round to rotate at 2 revolutions per minute(rpm)?

b) If the merry-go-round is initially rotating with a frequency of 2 rpm, then at what angular rate must it accelerate to be going 4 rpm after turning through one full rotation?

c) A force of 20 N is applied to the metal bar so that the merry-go-round begins to move. If there is a rock which rubs against the rim of the cylindrical merry-go-round causing a force of friction of 5 N in the direction opposite to the rotation, then calculate the angular acceleration of the merry-go-round.

d) What force must be applied to the metal bar in order to bring the merry-go-round to rest in 5 seconds if it is initially rotatating at 3 rpm?

3. Consider the yo-yo shown below. Assume the yo-yo is a solid cylinder of radius 2 cm and mass 0.5 kg (the rims are massless). It is released with no initial force.

a) What is the moment of inertia of the yo-yo?

b) What are the center of mass and angular accelerations of the yo-yo?

c) Explain what sort of force would be equired in order for the yo-yo to be in static equilibrium.

4. A certain 8000 kg space satellite is shown below. It can be considered a thin circular hoop of radius 10 m. It's main power consists of a pair of booster rockets which stick out a distance of 12 m from the axis of the satellite, and a pair of braking rockets located within the hoop (seven meters from the hoop axis).

a) If each of the 2 outer booster rockets provides a thrust of 500 N, and each of the 2 inner braking rockets provides a thrust of 100 N, then calculate the net torque on the satellite.

b) What is the moment of inertia for the satellite?

c) Find the angular acceleration of the satellite.

d) If the satellite is initially at rest, then what is its angular velocity after 20 seconds?

e) What is its tangential velocity after 20 seconds?

5.Consider a rotating solid sphere of radius 0.35 m and mass 2 kg, such as that used for a world globe.

a)You apply a 0.8 N tangential force with your finger at the equator of the globe. An opposing force of 0.5 N is applied by friction near the axis supports at a distance of 0.05 m from the axis of rotation. Find the angular acceleration.

b) Now you apply a force on the globe such that it acquires an angular acceleration of 0.08 rad/s2. Starting from rest, find the angular velocity of the globe after it has made 5 rotations.

c)What is the kinetic energy above of the globe after the 5 rotations in part b?

d) Find the tangential velocity of a point on the equator of the globe after the 5 rotations described in b.