Q. In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?
A.The same
B.Twice as much
C.Half as much
D.Four times as much
Solution
Angular momentum L = Iω; if one has twice the moment of inertia, it will have twice the angular momentum at the same angular velocity.
Q. In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?
A.LA = LB
B.LA = 2LB
C.LA = 4LB
D.LA = 1/2 LB
Solution
Angular momentum L = Iω; since IA = 2IB and ωA = ωB, LA = 2LB.
Q. The moment of inertia of a system of particles is calculated by summing which of the following?
A.Mass times distance from the axis
B.Mass times square of distance from the axis
C.Mass times angular velocity
D.Mass times linear velocity
Solution
The moment of inertia is calculated by summing the mass of each particle times the square of its distance from the axis of rotation: I = Σ(m_i * r_i²).
Correct Answer: B — Mass times square of distance from the axis
Q. Two particles A and B of masses m1 and m2 are moving in a circular path with angular velocities ω1 and ω2 respectively. What is the total angular momentum of the system?
A.m1ω1 + m2ω2
B.m1ω1 - m2ω2
C.m1ω1m2ω2
D.m1ω1 + m2ω2/2
Solution
Total angular momentum L = m1ω1 + m2ω2 for particles moving in the same direction.
Q. Two particles A and B of masses m1 and m2 are moving in a straight line with velocities v1 and v2 respectively. If they collide elastically, which of the following statements is true regarding their angular momentum about the center of mass?
A.It is conserved
B.It is not conserved
C.Depends on the masses
D.Depends on the velocities
Solution
Angular momentum about the center of mass is conserved in an elastic collision.
Q. Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about the origin?
A.m1v1 + m2v2
B.m1v1 - m2v2
C.m1v1 + m2(-v2)
D.m1v1 + m2v2
Solution
Total angular momentum L = m1v1 + m2(-v2) = m1v1 - m2v2.
Q. Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about a point O located at the center of mass?
A.(m1v1 + m2v2)
B.(m1v1 - m2v2)
C.m1v1 + m2v2
D.0
Solution
Total angular momentum is the sum of individual angular momenta, which is m1v1 + m2v2.
Q. Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about the origin if they are at a distance r from the origin?
A.m1v1r + m2v2r
B.m1v1r - m2v2r
C.m1v1r + m2(-v2)r
D.0
Solution
Total angular momentum L = m1v1r - m2v2r, but since they are in opposite directions, it simplifies to m1v1r + m2v2r.
Q. Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about a point O located at the midpoint between A and B?
A.(m1v1 + m2v2)r
B.(m1v1 - m2v2)r
C.0
D.(m1v1 + m2v2)/2
Solution
Since they are moving in opposite directions, the total angular momentum about point O is zero.
Q. Two particles A and B of masses m1 and m2 are moving with velocities v1 and v2 respectively. If they collide elastically, which of the following statements is true regarding their angular momentum about the center of mass?
A.It is conserved
B.It is not conserved
C.Depends on the masses
D.Depends on the velocities
Solution
Angular momentum is conserved in an elastic collision about the center of mass.
Q. Two particles of masses m1 and m2 are moving in a circular path of radius r with angular velocities ω1 and ω2 respectively. What is the total angular momentum of the system?
Q. Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?
A.m1r1/m2r2
B.m1/m2
C.r1/r2
D.m1r2/m2r1
Solution
Angular momentum L = mvr, thus L1/L2 = (m1r1)/(m2r2) when ω is constant.
Q. Two particles of masses m1 and m2 are moving in a straight line with velocities v1 and v2 respectively. If they collide elastically, what is the expression for the change in angular momentum about the center of mass?
A.m1v1 + m2v2
B.m1v1 - m2v2
C.0
D.m1v1 + m2v2 - (m1v1' + m2v2')
Solution
In an elastic collision, the total angular momentum about the center of mass is conserved.
Q. What is the angular momentum of a rolling object about its center of mass?
A.mv
B.Iω
C.mv + Iω
D.0
Solution
The angular momentum L of a rolling object about its center of mass is given by L = mv + Iω, where I is the moment of inertia and ω is the angular velocity.
Q. What is the condition for rolling without slipping?
A.v = Rω
B.v = 2Rω
C.v = 0
D.v = R^2ω
Solution
The condition for rolling without slipping is that the linear velocity v of the center of mass is equal to the product of the radius R and the angular velocity ω, i.e., v = Rω.
