Moment of Inertia
Q. If a rotating object has a moment of inertia of 5 kg·m² and is rotating with an angular velocity of 3 rad/s, what is its angular momentum?
A.
15 kg·m²/s
B.
5 kg·m²/s
C.
8 kg·m²/s
D.
10 kg·m²/s
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Solution
Angular momentum L is given by L = Iω. Thus, L = 5 kg·m² * 3 rad/s = 15 kg·m²/s.
Correct Answer: A — 15 kg·m²/s
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Q. If a rotating object has a moment of inertia of 5 kg·m² and is spinning with an angular velocity of 3 rad/s, what is its angular momentum?
A.
15 kg·m²/s
B.
5 kg·m²/s
C.
8 kg·m²/s
D.
10 kg·m²/s
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Solution
Angular momentum L = Iω = 5 kg·m² * 3 rad/s = 15 kg·m²/s.
Correct Answer: A — 15 kg·m²/s
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Q. If a rotating object has a moment of inertia of I and is rotating with an angular velocity ω, what is its rotational kinetic energy?
A.
1/2 Iω
B.
1/2 Iω^2
C.
Iω^2
D.
Iω
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Solution
The rotational kinetic energy is given by KE = 1/2 Iω^2.
Correct Answer: B — 1/2 Iω^2
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Q. If a solid cylinder is rotated about its diameter, what is its moment of inertia?
A.
1/2 MR^2
B.
1/4 MR^2
C.
1/3 MR^2
D.
MR^2
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Solution
The moment of inertia of a solid cylinder about its diameter is I = 1/4 MR^2.
Correct Answer: B — 1/4 MR^2
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Q. If a solid sphere and a hollow sphere have the same mass and radius, which one will roll down an incline faster?
A.
Solid sphere
B.
Hollow sphere
C.
Both will roll at the same speed
D.
Depends on the angle of incline
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Solution
The solid sphere will roll down the incline faster because it has a smaller moment of inertia compared to the hollow sphere.
Correct Answer: A — Solid sphere
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Q. If a solid sphere of mass M and radius R is rotating about an axis through its center, what is its moment of inertia?
A.
2/5 MR^2
B.
3/5 MR^2
C.
1/2 MR^2
D.
1/3 MR^2
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Solution
The moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.
Correct Answer: A — 2/5 MR^2
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Q. If a solid sphere of radius R and mass M is rotating about an axis through its center, what is its moment of inertia?
A.
2/5 MR^2
B.
3/5 MR^2
C.
1/2 MR^2
D.
1/3 MR^2
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Solution
The moment of inertia of a solid sphere about its center is I = 2/5 MR^2.
Correct Answer: A — 2/5 MR^2
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Q. If the moment of inertia of a body is 10 kg m², what is the angular momentum when it rotates with an angular velocity of 5 rad/s?
A.
50 kg m²/s
B.
10 kg m²/s
C.
5 kg m²/s
D.
2 kg m²/s
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Solution
Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.
Correct Answer: A — 50 kg m²/s
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Q. If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?
A.
125 J
B.
50 J
C.
100 J
D.
75 J
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Solution
Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.
Correct Answer: A — 125 J
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Q. If the moment of inertia of a body is 10 kg·m² and it is subjected to a torque of 20 N·m, what is the angular acceleration?
A.
2 rad/s²
B.
0.5 rad/s²
C.
5 rad/s²
D.
10 rad/s²
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Solution
Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².
Correct Answer: A — 2 rad/s²
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Q. If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.
Correct Answer: A — Doubles
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Q. If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by a factor of four
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Solution
Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.
Correct Answer: B — Halves
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Q. If the moment of inertia of a body is increased, what happens to its angular acceleration for a constant torque?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.
Correct Answer: B — Decreases
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Q. If the radius of a disc is doubled while keeping its mass constant, how does its moment of inertia change?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
The moment of inertia of a disc is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is quadrupled.
Correct Answer: C — It quadruples
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Q. If the radius of a disk is doubled while keeping its mass constant, how does its moment of inertia change?
A.
Increases by a factor of 2
B.
Increases by a factor of 4
C.
Remains the same
D.
Decreases by a factor of 4
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Solution
The moment of inertia of a disk is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is 4 times the original.
Correct Answer: B — Increases by a factor of 4
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Q. If the radius of a solid disk is doubled while keeping its mass constant, how does its moment of inertia change?
A.
Increases by a factor of 2
B.
Increases by a factor of 4
C.
Remains the same
D.
Decreases by a factor of 2
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Solution
The moment of inertia of a solid disk is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is 4 times the original.
Correct Answer: B — Increases by a factor of 4
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Q. If two identical disks are stacked on top of each other, what is the moment of inertia about the axis of the bottom disk?
A.
MR^2
B.
2MR^2
C.
1/2 MR^2
D.
4MR^2
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Solution
The moment of inertia of the bottom disk is MR^2, and the top disk contributes an additional MR^2 due to the parallel axis theorem, giving a total of 2MR^2.
Correct Answer: B — 2MR^2
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Q. If two rigid bodies have the same mass and shape but one is rotating faster than the other, how does their moment of inertia compare?
A.
The same
B.
The faster one has a larger moment of inertia
C.
The slower one has a larger moment of inertia
D.
Cannot be determined
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Solution
The moment of inertia depends only on the mass distribution and shape, not on the angular velocity.
Correct Answer: A — The same
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Q. The moment of inertia of a composite body can be calculated using which theorem?
A.
Pythagorean theorem
B.
Parallel axis theorem
C.
Perpendicular axis theorem
D.
Conservation of energy
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Solution
The moment of inertia of a composite body can be calculated using the parallel axis theorem.
Correct Answer: B — Parallel axis theorem
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Q. The moment of inertia of a hollow cylinder about its central axis is given by which formula?
A.
1/2 MR^2
B.
MR^2
C.
1/3 MR^2
D.
2/3 MR^2
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Solution
The moment of inertia of a hollow cylinder about its central axis is I = MR^2.
Correct Answer: B — MR^2
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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
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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
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Q. What happens to the moment of inertia of a rigid body if it is rotated about an axis that is not its principal axis?
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
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Solution
The moment of inertia can change when rotating about an axis that is not a principal axis due to the distribution of mass relative to the new axis.
Correct Answer: A — It increases
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Q. What is the moment of inertia of a disk of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
1/2 MR^2
B.
MR^2
C.
1/4 MR^2
D.
2/3 MR^2
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Solution
The moment of inertia of a disk about an axis through its center is I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a solid cylinder of mass M and radius R about its central axis?
A.
1/2 MR^2
B.
1/3 MR^2
C.
MR^2
D.
2/5 MR^2
Show solution
Solution
The moment of inertia of a solid cylinder about its central axis is given by I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a solid sphere of mass M and radius R about an axis through its center?
A.
2/5 MR^2
B.
3/5 MR^2
C.
1/2 MR^2
D.
MR^2
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Solution
The moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.
Correct Answer: A — 2/5 MR^2
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Q. What is the moment of inertia of a thin circular hoop of mass M and radius R about an axis through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a thin circular hoop about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
1/2 MR^2
B.
MR^2
C.
1/4 MR^2
D.
1/3 MR^2
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Solution
The moment of inertia of a thin circular plate about an axis through its center is I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis perpendicular to its plane through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
MR^2
B.
1/2 MR^2
C.
2/3 MR^2
D.
1/3 MR^2
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Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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