ANL - Uniform Circular Motion

Uniform Circular Motion

It is possible for an object to accelerate even if it is traveling at a constant speed. When an object travels at a constant speed through a circular pathway, the acceleration of the object is equal to the velocity squared divided by the radius of the path. The acceleration is directed toward the center of the pathway and causes a change in direction, not a change in speed. This is called the centripetal acceleration. The centripetal force is the mass times the centripetal acceleration. The force is also directed toward the center of the pathway. If an object does not maintain a constant speed while moving in a circular pathway, then a second component of acceleration is introduced that is applied at a tangent to the pathway of the object. The actual acceleration of the object would be determined by resolving the tangential acceleration and centripetal acceleration. Please watch the following presentation that will introduce the acceleration and forces acting on an object traveling through a circular pathway.

Uniform Circular Motion Practice

We will now practice solving problems using the concepts you learned in the presentation. Make sure that you are still showing all your work when you solve your problems. The presentation will give you time to work through the problems, find a solution, and check your work.

Uniform Circular Motion Self-Assessment

Now it is your turn. Complete the self-assessment questions to verify that you can apply the concept of centripetal acceleration and centripetal force. 

Problem 1 Image

  1. A 10 kg disk is placed on a horizontal frictionless table and tied to a string. The string passes through a hole in the center of the table and is tied to a mass M. The disk is then spun so that it has a speed of 25 m/s as it rotates around the hole in the table. What mass M, at the end of the string would allow the disk to rotate with a radius of 1.5 m? 

SOLUTION Links to an external site.

  1. A 25 kg ball is spun in an arc over the top of a girl's head. The radius of the ball around the center of the path is 2.2 m and it spins once every 1.5 seconds. What is the magnitude and direction of the tension on the rope used to spin the ball? 

SOLUTION Links to an external site.

  1. A 12 kg mass is tied to a string and spun in a vertical circle with a radius of 0.75m.  
    1. What is the minimum speed that the mass can have at the top of the circular pathway and still travel in the path?
    2. What would be the tension on the rope at that bottom of the circular path if itss velocity is now 6.1m/s?

SOLUTIONS Links to an external site.

Uniform Circular Motion Practice Problems

Download Uniform Circular Motion Practice Problems Links to an external site. for more practice. 

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

VIDEOS CREATED BY GAVS

IMAGES SOURCED FROM PUBLIC DOMAIN