Worksheet 16 –Rotation and Angular Momentum



Worksheet 16 –Rotation and Angular Momentum

1. A light flexible rope is wrapped around a solid cylinder of mass M and radius R, which rotates with no friction about a stationary horizontal axis. The free end of the rope is tied a mass m and the mass is released from rest, a distance h from the floor. Find the speed of the mass and the angular velocity of the cylinder just as mass m strikes the floor.

M

m

h

2. A solid bowling ball rolls without slipping down a ramp incline making an angle of 27( with the horizontal. What is the acceleration of the center of the bowling ball? Assume the bowling ball has mass 7.3 kg, and radius of 10cm.

3. Suppose the large disk of mass 2 kg, radius 0.2m and initial angular velocity of 50rad/s and a small disk with mass 4 kg, radius 0.1m and initial angular velocity of 200rad/s are pushed into one another. Find the common final angular velocity after the disks collide. Is kinetic energy conserved? Disk I = ½ Mr2

4. A girl stands at the center of a turntable, holding her arms out horizontally with a 5kg mass in each hand. She is set rotation about a vertical axis with an initial angular velocity of 1 revolution every 2 seconds.

A) Find her new angular velocity if she drops her hands to her sides. The girl’s inertia may be assumed constant at 6 kgm2. The original distance of the weights from the axis is 1 meter and their final distance is 0.2 m (look at the weights as particles about an axis).

B) Find her original rotational kinetic energy

C) Find her final rotational kinetic energy

D) Explain the results of answers B and C

5. A door that is 1 meter wide, has a mass of 15 kg, and is hinged at one side so it can rotate without friction about a vertical axis. A bullet having mass 10 grams and speed 400 m/s is fired into the door, in a direction perpendicular to the plane of the door, and embeds itself at the exact center of the door. Find the angular velocity of the door just after the bullet embeds itself. ( Idoor = 1/3 (ML2) )

6. A puck on a frictionless air hockey table has a mass of 0.05 kg and is attached to a cord passing through a hole in the table surface. The puck is originally revolving at a distance of 0.2 m from the hole, with an angular velocity of 3 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the puck revolves to 0.1m. The puck may be considered a point mass.

A) What is the new angular velocity

B) How much work was done by the person who pulled the cord?

7. A 5 kg block rests on a frictionless horizontal surface. A cord attached to the block passes over a pulley, whose diameter is 0.2 m, to a hanging block also of mass 5 kg. The system is released from rest, and the blocks are observed to move 4 meters in 2 seconds.

A) What was the tension in each part of the cord?

B) What was the moment of inertia of the pulley?

8. A yo-yo of mass 0.08 kg (considered a cylinder in shape) is being yo-yoed. The axle radius that the string is tied around is 2.5 mm and the radius of the yo-yo itself is 3.8cm. Ignore the rotational inertial created by the axle.

A) Determine the translational acceleration of the yo-yo if it is rolled down the string from rest.

B) Determine the tension in the string.

9. A thin spherical shell with mass of 2.7 kg and radius of 9.4 cm rolls from rest down a ramp whose length is 3.3 m. The ramp is inclined at an angle of 50( to the horizontal.

A) What is the shell’s linear speed when it reaches the bottom of the ramp?

B) What is the shell’s linear acceleration?

C) What is the shell’s angular acceleration?

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