Rolling Motion
Q. If a wheel of radius R rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?
A.
2πR
B.
πR
C.
4R
D.
R/2
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Solution
The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.
Correct Answer: A — 2πR
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Q. In rolling motion, which type of energy is associated with the rotation of the object?
A.
Translational kinetic energy
B.
Rotational kinetic energy
C.
Potential energy
D.
Elastic potential energy
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Solution
Rotational kinetic energy is associated with the rotation of the object in rolling motion.
Correct Answer: B — Rotational kinetic energy
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Q. What is the acceleration of a rolling object down an incline if the incline angle is θ?
A.
g sin(θ)
B.
g sin(θ)/2
C.
g sin(θ)/3
D.
g sin(θ)/4
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Solution
The acceleration of a rolling object down an incline is given by g sin(θ)/2, considering both translational and rotational motion.
Correct Answer: B — g sin(θ)/2
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Q. What is the angular momentum of a rolling object about its center of mass?
A.
mv
B.
Iω
C.
mv + Iω
D.
0
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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.
Correct Answer: C — mv + Iω
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Q. What is the condition for rolling without slipping?
A.
v = Rω
B.
v = 2Rω
C.
v = 0
D.
v = R^2ω
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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.
Correct Answer: A — v = Rω
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Q. What is the moment of inertia of a solid disk about its central axis?
A.
(1/2)MR^2
B.
(1/3)MR^2
C.
(1/4)MR^2
D.
MR^2
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Solution
The moment of inertia of a solid disk about its central axis is (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 about an axis through its center?
A.
(2/5)mr^2
B.
(1/2)mr^2
C.
(1/3)mr^2
D.
(5/2)mr^2
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Solution
The moment of inertia of a solid sphere about an axis through its center is given by I = (2/5)mr^2.
Correct Answer: A — (2/5)mr^2
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Q. What type of energy is primarily converted to kinetic energy when a rolling object descends a slope?
A.
Potential energy
B.
Thermal energy
C.
Elastic energy
D.
Chemical energy
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Solution
As the object descends, its gravitational potential energy is converted into kinetic energy.
Correct Answer: A — Potential energy
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Q. When a wheel rolls without slipping, what is the acceleration of its center of mass if it rolls down an incline with angle θ?
A.
g sin(θ)
B.
g sin(θ)/2
C.
g sin(θ)/3
D.
g sin(θ)/4
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Solution
The acceleration of the center of mass of a wheel rolling down an incline is g sin(θ).
Correct Answer: A — g sin(θ)
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Q. When a wheel rolls without slipping, what is the condition for the point of contact with the ground?
A.
It moves forward
B.
It is at rest
C.
It moves backward
D.
It accelerates
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Solution
The point of contact with the ground is momentarily at rest when the wheel rolls without slipping.
Correct Answer: B — It is at rest
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Q. When a wheel rolls without slipping, what is the relationship between the distance traveled by the center of mass and the angle rotated?
A.
d = Rθ
B.
d = 2Rθ
C.
d = R/2θ
D.
d = 3Rθ
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Solution
The distance traveled by the center of mass d is equal to the product of the radius R and the angle rotated θ in radians, i.e., d = Rθ.
Correct Answer: A — d = Rθ
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