Uniform Circular Motion

What is uniform circular motion? Movement of an object at constant speed

around a circle with a fixed radius Can the velocity be accelerated even though

it has constant speed? Yes, because the velocity may change due

to direction. If direction changes and velocity changes then an object can accelerate.

New terms for UCM

Term Symbol Units Example

Radius r m 3 m

Centripetal acceleration

ac m/s2 2.5 m/s2 toward the center

Tangential speed

vT m/s 3.6 m/s

Period T s 4.7 s

Centripetal force

Fc N 1.2 N toward the center

Describing Circular Motion

A lower case r represents the position of a vector (the radius of the circle)

The direction of the vector can change but not its length (length is proportional to magnitude, which is speed)

The acceleration of an object in uniform circular motion is always toward the center of the circle, called centripetal acceleration

Circular Motion Equations

Centripetal acceleration (ac)- acceleration of an object in uniform circular motion. • ac = vT

2/r

Tangential speed (vT)- speed at which an object travels in a circular path.• vT = 2πr/T

• an object will travel the distance of the circumference of the circle, which is represented by C = 2πr

• Time required for one complete revolution around a circle is called a period

– Symbol is T– Units are seconds

What about net force?

The force that causes centripetal acceleration is called centripetal force

For an object in UCM, what direction is the net force?

The same direction as the acceleration – toward the center

Fc = mac

If you stop the acceleration, what direction will the object move?

The movement of the object is in the direction of the velocity or tangent to the circle.