EMR - Angular Momentum

Angular Momentum

Angular momentum for any point is the cross product of the distance from the origin and the linear momentum of the object. Angular momentum is used to determine the change in angular velocity of objects after the mass, radius, or shape has changed.

The Law of Conservation of Angular Momentum states that if no net torque acts on a system, then the angular momentum of a system remains constant.

When applied to rotating objects the angular momentum is the moment of inertia times the angular velocity of the objects. The direction of the angular momentum is perpendicular to the plane of rotation and can be determined using the right hand rule.

Please watch the following presentation that will discuss Angular Momentum. 

Angular Momentum Practice

Now we will do some practice problems applying the conservation of Angular Momentum. Please watch the following presentation of some example problems.

Angular Momentum Self-Assessment

Now it's your turn. Complete the following Angular Momentum problems to verify that you understand how to apply the Angular Momentum equations to different situations.

  1. A puck with a mass of 10 kg is tied to a massless string and placed on a table. The table has a small hole that allows the string to go through the table so that the radius of the spinning puck can be changed. The puck is set spinning with an angular velocity of 7 rad/s with a radius of 1.5 m.

Problem 1 Image

    1. What is the linear velocity of the puck?
    2. What is the tension on the string?
    3. The string is allowed to lengthen until the radius of the puck's spin is 2m. What is the angular velocity of the puck?
  2.  4 kids each with a mass of 55kg are standing on the edge of a merry-go-round.  The merry-go-round has a mass of 100kg, a radius of 1.75m, and is rotating at 3.2 rad/s.  Treat each of the kids as a point mass and treat the merry-go-round as a solid disk. 
    1. Three of the kids jump off.  What is their linear velocity as they strike the ground?
    2. Assuming they are each brought to a stop in 2.7 m, what is the coefficient of friction between the ground and each kid?
    3. What is the angular velocity of the kid that is still on the merry-go-round?
    4. What force would be required to keep the girl spinning on the ride?
  3. A skater spins at 2 rad/s with her arms extended. We will model her body as a cylinder spinning around its central axis. Her body has a mass of 50kg and a radius of 12 cm.  We will model her arms as rods pivoting around one end. Her arms are each 75 cm long and each have a mass of 4 kg.   If she pulls her arm into her body (adding the mass to the cylinder), what is her new angular velocity?

SOLUTIONS 1, 2, & 3 Links to an external site.

Angular Momentum Practice Problems

Download Angular Momentum Practice Problems Links to an external site. for more practice.

Download solutions Links to an external site. to the practice problems. 

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