Q. A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?
A.It doubles
B.It halves
C.It remains the same
D.It quadruples
Solution
Angular momentum L = Iω. If I is doubled and ω remains constant, L also doubles.
Q. A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be the new angular momentum?
A.L
B.2L
C.4L
D.L/2
Solution
Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.
Q. A rotating object has an angular momentum of L. If its moment of inertia is doubled while keeping the angular velocity constant, what will happen to its angular momentum?
A.It doubles
B.It halves
C.It remains the same
D.It becomes zero
Solution
Angular momentum L = Iω; if I is doubled and ω remains constant, L remains the same.
Q. A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
A.L
B.2L
C.4L
D.L/2
Solution
New angular momentum L' = I'ω' = (1/2 I)(2ω) = Iω = L.
Q. A rotating object has an angular momentum of L. If its moment of inertia is halved and its angular velocity is doubled, what is the new angular momentum?
Q. A satellite is in a circular orbit around the Earth. What is the angular momentum of the satellite if its mass is m, its orbital radius is r, and its orbital speed is v?
A.mv^2/r
B.mvr
C.mr^2
D.mv
Solution
Angular momentum L = mvr, where v is the orbital speed and r is the radius of the orbit.
Q. A solid cone rolls down an incline. If its height is h, what is the relationship between its potential energy and kinetic energy at the bottom?
A.PE = KE
B.PE = 2KE
C.PE = 3KE
D.PE = 4KE
Solution
For a solid cone rolling down an incline, the potential energy at height h is converted into translational and rotational kinetic energy, leading to PE = 2KE.
Q. A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one will have a greater speed at the bottom?
A.Solid cylinder
B.Hollow cylinder
C.Both have the same speed
D.Depends on the mass
Solution
The solid cylinder has a smaller moment of inertia compared to the hollow cylinder, thus it will have a greater speed at the bottom.
Q. A solid cylinder of radius R rolls down a frictionless incline. What is the ratio of its translational kinetic energy to its total kinetic energy at the bottom?
A.1:1
B.2:1
C.1:2
D.3:1
Solution
At the bottom, total kinetic energy = translational + rotational. For a solid cylinder, the ratio of translational to total kinetic energy is 2:1.
Q. A solid cylinder rolls down an incline of height h. What fraction of its total mechanical energy is kinetic energy at the bottom?
A.1/3
B.1/2
C.2/3
D.1
Solution
At the bottom, total mechanical energy is converted into kinetic energy, which is the sum of translational and rotational kinetic energy. For a solid cylinder, 2/3 of the energy is kinetic.
Q. A solid sphere and a hollow sphere of the same mass and radius are released from rest at the same height. Which one reaches the bottom first?
A.Solid sphere
B.Hollow sphere
C.Both reach at the same time
D.Depends on the surface
Solution
The solid sphere reaches the bottom first because it has a lower moment of inertia, allowing it to convert more potential energy into translational kinetic energy.
