This document contains a quiz with multiple choice and free response questions covering rotational motion and dynamics concepts like moment of inertia, centripetal force, angular momentum, and gravitational forces. The multiple choice section has 15 questions testing definitions and applications. The free response section asks students to explain concepts like moments of inertia and circular motion scenarios. Several calculations are also provided in the exercises section to evaluate skills in rotational kinematics and dynamics equations.

1. QUIZ 4:
MULTIPLE CHOICES (10%)
1. A solid disk rolls from rest down an inclined plane. A hole is then cut in the center of the disk, and the resulting doughnut-shaped object is
allowed to roll down the same inclined plane. Its speed at the bottom of the plane is:
a. Less than that of the solid disk c. Greater than that of the solid disk
b. The same as that of the solid disk d. Any of the above, depending on the size of the hole
2. The shape of the earth is closes to that of
a. A perfect sphere b. A foot ball c. An egg d. A grapefruit
3. The rotational analog of force in linear motion is
a. Moment of inertia b. Angular momentum c. Torque d. Weight
4. In an elastic collision:
a. Momentum is conserved but not KE c. Momentum and KE are both conserved
b. KE is conserved but not momentum d. Neither momentum nor KE is conserved
5. A solid iron sphere A rolls down an inclined plane, while an identical sphere B slides down the plane in a frictionless manner.
a. Sphere A reaches the bottom first c. They reach the bottom together
b. Sphere B reaches the bottom first d. Which one reaches the bottom first depend on the angle of the plane
6. At the bottom of the plane, the total KE of sphere A in item number 5 is:
a. Less than that of sphere B c. More than that of sphere B
b. Equal to that of sphere B d. More or less than that of sphere B, depending on the angle of the plane
7. The acceleration of an object undergoing uniform circular motion is constant in:
a. Magnitude only c. Neither magnitude and direction
b. b. Direction only d. Both magnitude and direction
8. The speed needed to put a satellite in orbit does not depend on:
a. The radius of the orbit b. The shape of the orbit c. The value of g at the orbit d. the mass of satellite
9. An astronaut is “weightless” in a spacecraft
a.As it takes off from the earth c. in all orbits
b. In certain orbits only d. Only when the escape speed is exceeded
10. The gravitational acceleration of an object
a. Has the same value everywhere in space c. Varies somewhat over the earth’s surface
b. Has the same value everywhere on the earth’s surface d. Is greater on the moon because of its diameter
11. A hole is drilled to the center of the earth and a stone is dropped into it. When the stone is at the earth’s center, compared with the values at
the earth’s surface:
a. Its mass and weight are both unchanged c. Its mass is unchanged and its weight is zero
b. Its mass and weight are both zero d. Its mass is zero and its weight is unchanged
12. If the earth were three times farther from the sun than it is, the gravitational force exerted on it by the sun would be:
a. Three times as large as it is now c. One-third as large as it is now
b. Nine times as large as it is now d. One-ninth as large as it is now
13. The centripetal acceleration of a particle of a circular motion
a. Is less than its tangential acceleration c. Is more than its tangential acceleration
b. Is equal to its tangential acceleration d. may be more or less than its tangential acceleration
14. The rotational analog of mass in linear motion is:
a.Moment of inertia b. Angular momentum c. Torque d. Angular speed
15. A quantity not directly involved in the rotational motion of an object is:
a.
Mass b. Moment of inertia c. Torque d. Angular speed
QUESTIONS: (20%)
1. A square and a rectangle of the same mass are cut from a sheet metal. Which has the greater moment of inertia about a perpendicular axis
through its center? The rectangle
2. A hollow cylinder and a solid cylinder having the same mass and diameter are released from rest simultaneously at the top of an inclined
plane. Which reaches the bottom first? The solid cylinder reaches the bottom first because its moment of inertia is smaller and hence less of
its initial PE becomes KE of rotation.
3. Under what circumstances, if any, can an object move in a circular path without being accelerated? Under no circumstances
4. A track team on the moon could set new records for the high jump (if they did not need space suits, of course) because of the smaller
gravitational pull there. Could sprinters also improve their times for the 100-m dash? The mass of a sprinter and the force his or her legs can
exert are both unchanged on the moon. Hence the acceleration is unchanged and the time needed would not be different.
5. A person swings an iron ball in a vertical circle at the end of a string. At what point in the circle is the string most likely to break? Why? At the
bottom of the circle, where the string must support all the ball’s weight as well as provide centripetal force.
EXERCISES: (30%)
1. A phonograph record 12 inches in diameter rotates 33-1/3 times per minute. (a) What is the linear speed of a point on its rim? (b) What is
the centripetal acceleration of a point on its rim? Ans. 1.7 ft/s, 6.1 ft/s2.
2. Find the momentum of a 3200 lb car moving at 30 mph. Ans. 4400 slug – ft/s
3. A physics teacher swings a pail of water in a vertical circle 4.0 ft in radius at constant speed. What is the maximum time per revolution if the
water is not to spill? 2.2 sec
4. An apple pie is cut into nine equal pieces. What angle (in radians) is included between the sides of each piece? Ans. 0.698 rad
5. What is the angular speed in rad per second of the hour, minute and seconds hand of a clock? Ans. 1.45x10-4 rad/s, 1.75x10-3 rad/s, 0.105
rad/s
6. In 1941, a wind-driven electric power station was set up at Grandpa’s Knob, Vermont. The propeller was 40 m in diameter. When the
propeller was turning at 30 rev/min, what was the linear speed of one of the blade tips in kilometers per hour? Ans. 226 kph
7. A truck undergoes an acceleration of 0.25 m/s2. If its wheels are 1.0 m in diameter, what is their angular acceleration? Ans. 0.5 rad/s2
8. A torque of 500 N-m is applied to a turbine rotating at 200 rad/s. After 40 sec its speed has doubled. What is the turbine’s moment of inertia?
Ans. 100 kg-m2
9. A rotating platform is to be used to test aircraft equipment under accelerations of 6g. If the equipment is 50 cm from the axis, what angular
speed is needed? 11 rad/s
10. A ball of mass m is swung in a vertical circle on a string just fast enough for the string to be barely taut at the top of the circle. Find the
tension in the string at the bottom of the circle. Ans. 5mg