Animation 3.5: Angular Momentum

The simulation shows a mass tethered by a rope to a fixed point. The mass is given an initial velocity, and the rope begins to coil around the central pole. As the radius of the circle shrinks, the mass moves faster. Since angular momentum depends on the speed, mass, and also the distance to the center of spin, the speed of the object increases as the radius of spin decreases. Because there are no outside forces acting, the angular momentum of the mass is constant.

 

Questions

  1. The magnitude of angular momentum for an object rotating about a specific point is equal to the product of its mass, speed, and distance from the point (angular momentum = m v r). Does this relationship between speed and distance appear to hold for this simulation, where the angular momentum is constant?
  2. .
  3. The principles of energy, linear momentum, and angular momentum all originate in Newton’s laws. Conservation of angular momentum is one way to explain the increase in speed of the object. Can you explain the increase in speed of the object based on force and acceleration concepts? (Hint: review Section 2-12 of the text.)
  4. Can you explain the increase in speed of the object based on work and energy principles? (Hint: The force of the last question is acting in the same direction as the change in radial distance.)
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