605 Centripetal Force

If an angle of 90° is maintained between the (net) force and the velocity of an object, only the direction of the velocity changes. The speed does not. The resulting motion is uniform circular motion.

centripetalForce0

The magnitude of the required centripetal force is related to the speed and radius of circular motion by the formula m\frac{{{v}^{2}}}{r}.

For the same v, a stronger centripetal force F would result in a tighter circular motion. In the animation below, the objects are experiencing centripetal forces of 4F, 2F and F, resulting in circular motion of radii R, 2R and 4R.

centripetalForce1

For the same F, a lower speed v would result in a tighter circular motion. In the animation below, the objects have speeds of 1/√2 v, v and √2v, resulting in circular motion of radii R, 2R and 4R.

centripetalForce

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s