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8 Rotational Equilibrium and Rotational Dynamics
8.6 Practice Quiz 8.2
Choose the best answer. Answers can be found at the back of the book.
1. If the perpendicular distance between the axis of rotation and a particle is multiplied by a factor of 5 , then the moment of inertia of mthe particle will be multiplied by a factor of
A. 5 B. 25 C. 0.04 D. 0.2 E. 2.236
2. An object is said to be in translational equilibrium if
A. it is either at rest or moving with a constant acceleration B. it is either at rest or moving with a constant speed
C. it is either at rest or rotating with a constant angular acceleration.
D. it is either at rest or moving in a straight line with a constant speed.
E. it is either at rest or rotating with a constant angular velocity.
3. An object of mass 7.3 kg is revolving in a circular path of radius 6.4 m. Calculate its moment of inertia about an axis of rotation perpendicular to the plane of the circle passing through the center of the circle.
A. 328.909 kg m 2 B. 239.206 kg m 2 C. 299.008 kg m 2 D. 209.306 kg m 2 E. 418.611 kg m 2
4. Three particles of masses 6.3 kg, 5.5 kg and 3.7 kg are located at the points (9, -1) m, (-2, -2) m, and (8, 2) m respectively. Calculate the moment of inertia of these system of particles if the axis of rotation is the x-axis.
A. 25.86 kg m 2 B. 43.1 kg m 2 C. 47.41 kg m 2
165 D. 56.03 kg m 2
E. 34.48 kg m 2
5. Three particles of masses 5.3 kg, 10.5 kg and 1.7 kg are located at the points (15, 0) m, (-5, 0) m, and (2, 1) m respectively. Calculate the rotational kinetic energy of this system of particles if they are revolving around the x-axis with an angular velocity of 9 rad ⁄ s.
A. 61.965 J B. 96.39 J C. 68.85 J D. 48.195 J E. 82.62 J
6. Three particles of masses 1.3 kg, 7.5 kg and 7.7 kg are located at the points (9, 2) m, (-2, -5) m, and (-10, 2) m respectively. Calculate the angular momentum of this system of particles if they are revolving around the y-axis with an angular velocity of 3 rad ⁄ s.
A. 2715.9 J s B. 3259.08 J s C. 1901.13 J s D. 2444.31 J s E. 3802.26 J s
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166
7. A spherical object of mass 4 kg and radius 0.024 m is rolling on a horizontal surface with a speed of 2.5 m ⁄ s. Calculate its kinetic energy. (Ispher = 2MR 2 / 5)
A. 19.25 J B. 24.5 J C. 21 J D. 12.25 J E. 17.5 J
8. A spherical object of mass 1 kg and radius 0.028 m is rolling down an inclined plane of length 5 m that makes an angle of 60 deg with the ground. Calculate its speed by the time it reaches the ground (Ispehre = 2MR 2 / 5)
A. 7.786 m ⁄ s B. 10.122 m ⁄ s C. 9.343 m ⁄ s D. 10.9 m ⁄ s E. 7.007 m ⁄ s
9. The angular momentum of a spherical object revolving about an axis passing through its center increased from 9 J s to 24 J s in 5 s. Calculate the torque acting on it.
A. 4.2 N m B. 3 N m C. 2.4 N m D. 3.9 N m E. 3.3 N m
10. Two particles of masses 10 kg and 21 kg located at x = 1.3 m and x = -1.8 m on the x-axis (connected by a rod of negligible mass) are revolving about the y-axis with an angular speed of 6.5 rad ⁄ s. If the 10 kg particle slides to the new location x = 0.7, Calculate the new angular speed with which the system is revolving.
A. 8.326 rad ⁄ s B. 10.597 rad ⁄ s C. 5.299 rad ⁄ s D. 7.569 rad ⁄ s E. 9.083 rad ⁄ s
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