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Physics

WSD Angular Kinematics (7)

Show all work for full credit and underline your final answer on a separate paper

  1. A model airplane is kept in a circular path by means of a control line. The airplane starts at rest and reaches an angular speed of 3.33 rad/s after a constant angular acceleration of 0.183 rad/s2. How long does it take the airplane to reach its final angular speed?
  2. A millstone is a large stone wheel once used to grind grain for flour. Suppose a stone in a windmill is moved from rest with a constant angular acceleration of 0.13 rad/s2. How long does it take the millstone to move through an angular displacement of 1.6 rad?
  3. A ceiling fan’s angular speed increases from 5.2 rad/s to 20.9 rad/s. During this constant angular acceleration, the fan moves through an angular displacement of 216 rad. How long does it take the fan to reach its final angular speed?
  4. A runner on a circular track increases his angular speed from 0.111 rad/s to 0.178 rad/s. If the runner’s angular acceleration is 1.1 x 10-2rad/s2, what is his angular displacement?
  5. Even rarer than phonograph turntables for long-playing (LP) records are those turntables used in the first half of the twentieth century. Unlike the LP turntables, which rotated at 33.3 rev/min, these older turntables turned at 78.0 rev/min. suppose a turntable with this angular speed is shut off, so that it comes to a stop 30.0 s later. If the turntable has a constant angular acceleration of –0.272 rad/s2, what is its angular displacement? Give your answer in both radians and number of revolutions.
  6. A rotary saw with an angular speed of 298 rad/s cuts through a piece of wood. The saw undergoes a constant angular acceleration of –44.0 rad/s2 while it goes through an angular displacement of 276 rad. What is the saw’s final angular speed?
  7. The lumberjack sport of logrolling, or birling, involves two competitors running along the circumference of a floating log. Each competitor tries to alter the log’s speed in such a way that the other competitor will fall into the water. Suppose a lumberjack is practicing logrolling skills alone on a log. Initially at rest, the log undergoes a constant angular acceleration, so that after 13.0 s the log has turned through 10.0 rev. What is the final angular speed of the log in rad/s?
  8. An automobile engine’s angular speed is increased from 1200 rev/min to 3600 rev/min in 12 s. What is the engine’s angular acceleration in rad/s 2?
  9. The drive wheel on a vacuum pump has an angular displacement of 158 rad as it accelerates from rest to 70.0 rad/s. What is the wheel’s angular acceleration?
  10. A pet hamster runs inside its exercise wheel. The wheel has an initial angular speed of 3.29 rad/s. Over the next 2.50 s, the hamster increases its speed and the wheel undergoes a constant angular acceleration. If the angular displacement of the wheel during this time is 12.3 rad, what is the wheel’s angular acceleration?