Rotational Inertia Multiple Choice Questions Answers - Set 05 - ObjectiveBooks

Practice Test: Question Set - 05

1. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular velocities after a given time t, least to greatest.
(A) Disk, hoop, sphere
(B) Hoop, disk, sphere
(C) Hoop, sphere, disk
(D) Hoop, disk, sphere

2. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:
(A) Decreases in magnitude and becomes more nearly tangent to the rim
(B) Decreases in magnitude and becomes more nearly radial
(C) Increases in magnitude and becomes more nearly tangent to the rim
(D) Increases in magnitude and becomes more nearly radial

3. The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration, in rad/s2 of this wheel is:
(A) 4π/2
(B) 2π
(C) 1/30
(D) 2π/30

4. A wheel initially has an angular velocity of 36 rad/sec but after 6.0sec its angular velocity is 24 rad/sec. If its angular acceleration is constant the value is:

5. A wheel initially has an angular velocity of 18 rad/sec but it is slowing at a rate of 2.0 rad/s². By the time it stops it will have turned through:
(A) 13 rev
(B) 26 rev
(C) 39 rev
(D) 52 rev

6. A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s². The cord will unwind in:

(A) 0.82 sec
(B) 2.0 sec
(C) 8.0 sec
(D) 16 sec

7. Two wheels are identical but wheel ‘B’ is spinning with twice the angular velocity of wheel ‘A’.  The ratio of the radial acceleration of a point on the rim of ‘B’ to the radial acceleration of a point on the rim of ‘A’ is:
(A) 1
(B) 2
(C) 1/2
(D) 4

8. Ten seconds after an electric fan is turned on, the fan rotates at  300 rev/min. Its average angular acceleration is:
(C) 30 rev/sec2
(D) 50 rev/min2

9. The acceleration of a point on a spinning wheel is increased by a factor of 4 if:
(A) The angular velocity and the angular acceleration are each increased by a factor of 4
(B) The angular velocity is increased by a factor of 4 and the angular acceleration is not changed
(C) The angular velocity and the angular acceleration are each increased by a factor of 2
(D) The angular velocity is increased by a factor of 2 and the angular acceleration is increased by a factor of 4

10. A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5) MR2. A light string of length 2R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:
(A) (2/5) MR²
(B) 4 MR2
(C) (7/5) MR2
(D) (47/5) MR2

11. A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:
(A) Applying the force near the axle, radially outward from the axle
(B) Applying the force near the rim, radially outward from the axle
(C) Applying the force near the axle, parallel to a tangent to the wheel
(D) Applying the force at the rim, tangent to the rim

12. A grinding wheel, used to sharpen tools, is powered by a motor. A knife held against the wheel exerts a torque of 0.80 Nm. If the wheel rotates with a constant angular velocity of 20 rad/s the work done on the wheel by the motor in 1.0 min is:
(A) 0
(B) 480 J
(C) 960 J
(D) 1400 J

13. String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. If the string is pulled out at a constant rate of 10 cm/sec and does not slip on the cylinder, the angular velocity of the cylinder is: