Moment of Inertia
KErotational
Torque
Newton's 2nd Law
Angular Momentum
Miscellaneous
100
Two uniform disks have the same radius but different masses: disk 1 has a mass M, disk 2 has a mass 2M. What is the ratio of the moment of inertia of the first disk to the second disk?
1:2
100
A solid cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s moment of inertia (I) about the axis is 6.0 kg-m2. At time t = 0 s, the cylinder is at rest. At time, t = 2.0s, its angular velocity is 2.0 rad/s.What is the rotational kinetic energy of the cylinder at t = 2 s?
12J
100
Torque is the rotational analog of which of the following quantities?
A. kinetic energy
B. linear momentum
C. acceleration
D. force
D. force
100
In translational motion, mass is a measure of an object’s acceleration in response to a force. What is the rotational analog of mass?
a. torque
b. moment of inertia
c. angular acceleration
d. angular momentum
b. moment of inertia
100
An ice skater performs a fast spin by pulling her outstretched arms down and close to her body. What happens to her angular momentum with respect to the axis of rotation?
a. increases
b. decreases
c. stays the same
d. depends on her initial rotational velocity
c. stays the same
100
The Earth moves around the Sun in an elliptical orbit. As the Earth approaches its closest point to the Sun in its orbit, the Earth’s linear velocity increases. Which of the following doesn’t change in the Earth-Sun system?
a. orbital radius
b. kinetic energy
c. potential energy
d. angular momentum
d. angular momentum
200
Two uniform disks have the same mass but different radii: disk 1 has a radius R and disk 2 has a radius 2R. What is the ratio of the moment of inertia of the first disk to the second disk?
1:4
200
Which of the following objects has the greatest rotational kinetic energy if they all have the same mass & radius?
A) cylinder
B) sphere
C) hoop
D) all have the same
E) not enough information
C) hoop
More mass farther from the center → harder to rotate → more energy stored in rotation.
200
If the 6.0 kg mass is 4.0 m away from the pivot, how far away is the 10.0 kg mass if the system is not rotating? 
2.4m
200
When a solid object rotates with a constant angular acceleration, which of the following is true?
a. All points on the object rotate with the same centripetal acceleration.
b. The net torque applied to the object must be zero.
c. The net torque applied to the object must be a constant.
d. All points on the object rotate with the same tangential acceleration.
c. The net torque applied to the object must be a constant.
200
A solid cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s moment of inertia (I) about the axis is 6.0 kg-m2. At time t = 0 s, the cylinder is at rest. At time, t = 2.0 s, its angular velocity is 2.0 rad/s.What is the angular momentum of the cylinder at t = 2 s?
12 kg-m2/s
200
Two boxes of mass 10 kg and 18 kg are on either side of the pivot, as shown below.
At what distance d should the 18 kg mass be kept so that the two sides are balanced about the pivot?
15cm
300
A solid sphere of mass m is fastened to another sphere of mass 2m by a thin rod with a length of 3x. The spheres have negligible size, and the rod has negligible mass. What is the moment of inertia of the system of spheres as the rod is rotated about the point located at position x, as shown?
9 mx2
300
An experiment is performed in a physics class where three objects, an empty can, a D battery and a marble, roll down an incline of height, H without slipping. A box slides down an adjacent frictionless incline of the same height. Which of the four objects reaches the bottom of their inclined planes first?
a. empty can c. marble
b. battery d. box
d. box
300
In the diagram, two boxes with masses, 3 kg and 9 kg are attached to the ends of a 1 m long lever. At which of the following points should the lever be placed on a fulcrum in order to keep the lever at equilibrium.
D
300
A wheel with rotational inertia, I is placed on an axle and is free to rotate without friction. The angular speed, ω of the wheel is increased from zero to ωf in a time interval, t. What is the average net torque on the wheel during this time interval?
300
A baseball player swings his bat with his arms fully extended. If his arms are pulled in closer to his body, which of the following choices correctly describes the impact of his motion on his swing’s angular momentum and kinetic energy?
c. Angular Momentum remains constant
Kinetic Energy increases
300
A uniform wooden board of mass 10 M is held up by a nail hammered into a wall. A block of mass M rests L/2 away from the pivot. Another block of a certain mass is hung a distance L/3. The system is in static equilibrium. What is the measure of the mass labeled "?" ?
3/2 M
400
The moment of inertia of a rod of length L about its center of mass is Icm =1/12ML2.What is the rod’s moment of inertia when it is rotated at a point L/4 away from the center?
7/48 ML2
Use the Parallel Axis Theorem
400
An ice skater performs a fast spin by pulling her outstretched arms down and close to her body. What happens to her kinetic energy?
a. increases
b. decreases
c. stays the same
d. depends on her initial rotational velocity
a. increases
400
You are choosing a screwdriver to loosen a stuck screw. In addition to selecting a screwdriver with a larger blade, which of the following qualities of the screwdriver will allow you to deliver the most torque to the screw?
a. longer length of the screwdriver shank
b. handle with a small diameter
c. handle with a large diameter
d. shorter length of the screwdriver shank
c. handle with a large diameter
- (a) longer shank → does not increase torque (axis is along the shaft) ❌
- (b) small handle diameter → smaller r, less torque ❌
- (c) large handle diameter → larger r, more torque ✅
- (d) shorter shank → no effect on torque ❌
400
A cylindrical object is fixed about a line passing through its axis. It is set into motion by applying a torque. The angular velocity of the cylinder increases to 0.8 rad/s in 2 s. If the moment of inertia of the cylinder is equal to 4 kgm2, what is the average torque acting on the cylinder?
1.6Nm
400
The above is an exaggerated view of the Earth’s elliptical orbit about the Sun (it is actually very close to a circle). As it moves from point A to point B, which of the following is true about the Earth’s speed and angular momentum?
d. speed decreases
angular momentum remains constant
400
The moment of inertia of a cylinder of mass M and radius R is ½ MR2 when the axis of rotation passes through its center. What is the moment of inertia of the cylinder about the axis of rotation tangent to the cylinder?
3/2 MR2
Parallel Axis Theorem
500
Three objects of masses 2 kg,3 kg, and 1.5 kg are in a 2D coordinate system having coordinates (1,1),(0,−2), and (3,4). What is the moment of inertia of the system consisting of these three particles for an axis passing through the origin?
(Assume the coordinates are in meters)
53.5 kgm2
500
What is the moment of inertia of a spinning object of radius 0.5 m and mass 6 kg moving at 5 m/s, if it has a kinetic energy of 100 J?
1/2 kg-m2
500
A wooden square of side length 1.0 m is on a horizontal tabletop and is free to rotate about its center axis. The square is subject to two forces and rotates. Find the net torque on the system.
* The lever arm is the vertical distance
Left Force: torque=4N (.5m)=2N-m clockwise
Right Force: torque = 8N(.5m)=4N-m counterclockwise
Net Torque = 2N-m
500
Two masses, one with mass m, and the other with mass 2m, are attached to a light rigid rod as shown. When the system is released from rest, the rod begins to rotate with an angular acceleration of _____.
a. −𝑔/4𝑙 c. −𝑔/5𝑙
b. −𝑔/7𝑙 d. −𝑔/9𝑙
d. −𝑔/9𝑙
500
A certain star, of mass m and radius r, is rotating with a rotational velocity . After the star collapses, it has the same mass but with a much smaller radius. Which statement below is true?
a. The star's moment of inertia I has decreased, and its angular momentum L has increased.
b. The star's moment of inertia I has decreased, and its angular velocity has decreased.
c. The star's moment of inertia I remains constant, and its angular momentum L has increased.
d. The star's angular momentum L remains constant, and its rotational kinetic energy has decreased.
e. The star's angular momentum L remains constant, and its rotational kinetic energy has increased.
e. The star's angular momentum L remains constant, and its rotational kinetic energy has increased.
500
A thin stick of length 30 cm is made to rotate either about point X or Y. The forces acting on the stick are as follows.
What is the net torque acting on the stick about an axis passing through X?
2.43Nm or 243Ncm