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Rotational Dynamics: Angular Velocity and Acceleration Analysis

Explore graphs of angular velocity and acceleration to determine maximum speeding up rate in rotation.

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Rotational Dynamics: Angular Velocity and Acceleration Analysis

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  1. Q9.1 The graph shows the angular velocity and angular acceleration versus time for a rotating body. At which of the following times is the rotation speeding up at the greatest rate? 1. t = 1 s 2. t = 2 s 3. t = 3 s 4. t = 4 s 5. t = 5 s

  2. A9.1 The graph shows the angular velocity and angular acceleration versus time for a rotating body. At which of the following times is the rotation speeding up at the greatest rate? 1. t = 1 s 2. t = 2 s 3. t = 3 s 4. t = 4 s 5. t = 5 s

  3. Q9.2 A DVD is initially at rest so that the line PQ on the disc’s surface is along the +x-axis. The disc begins to turn with a constant az = 5.0 rad/s2. At t = 0.40 s, what is the angle between the line PQ and the +x-axis? 1. 0.40 rad 2. 0.80 rad 3. 1.0 rad 4. 2.0 rad

  4. A9.2 A DVD is initially at rest so that the line PQ on the disc’s surface is along the +x-axis. The disc begins to turn with a constant az = 5.0 rad/s2. At t = 0.40 s, what is the angle between the line PQ and the +x-axis? 1. 0.40 rad 2. 0.80 rad 3. 1.0 rad 4. 2.0 rad

  5. Q9.3 A DVD is rotating with an ever-increasing speed. Compared to the point P on the disc’s surface, the point Q on the disc’s surface has 1. the same centripetal acceleration and the same tangential acceleration 2. a greater centripetal acceleration and a greater tangential acceleration 3. a smaller centripetal acceleration and a smaller tangential acceleration 4. a greater centripetal acceleration and the same tangential acceleration 5. none of the above

  6. A9.3 A DVD is rotating with an ever-increasing speed. Compared to the point P on the disc’s surface, the point Q on the disc’s surface has 1. the same centripetal acceleration and the same tangential acceleration 2. a greater centripetal acceleration and a greater tangential acceleration 3. a smaller centripetal acceleration and a smaller tangential acceleration 4. a greater centripetal acceleration and the same tangential acceleration 5. none of the above

  7. Q9.4 Compared to a gear tooth on the rear sprocket (on the left, of small radius) of a bicycle, a gear tooth on the front sprocket (on the right, of large radius) has 1. a faster linear speed and a faster angular speed 2. the same linear speed and a faster angular speed 3. a slower linear speed and the same angular speed 4. the same linear speed and a slower angular speed 5. none of the above

  8. A9.4 Compared to a gear tooth on the rear sprocket (on the left, of small radius) of a bicycle, a gear tooth on the front sprocket (on the right, of large radius) has 1. a faster linear speed and a faster angular speed 2. the same linear speed and a faster angular speed 3. a slower linear speed and the same angular speed 4. the same linear speed and a slower angular speed 5. none of the above

  9. Q9.5 All three of these objects are uniform, have the same mass, and have the same outer dimension. Which has the smallest moment of inertia about an axis through its center as shown? 1. the solid cylinder 2. the hollow cylinder 3. the rectangular solid 4. not enough information given to decide

  10. A9.5 All three of these objects are uniform, have the same mass, and have the same outer dimension. Which has the smallest moment of inertia about an axis through its center as shown? 1. the solid cylinder 2. the hollow cylinder 3. the rectangular solid 4. not enough information given to decide

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