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.

Describing Circular Motion

A lower case r represents the position of a vector

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

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

Equations

ac = v2/r

One complete revolution around a circle is called a period– Symbol is T

– Units are seconds

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

v = 2πr/T

Combining Equations

If we substitute the previous formula for v in the original formula for centripetal acceleration we would get

ac = 4π2r/T2

Sometimes the force that causes centripetal acceleration is called centripetal force

Which direction is the net force? The same direction as the acceleration

Fnet = mac

Fnet = mv2/r

Fnet = m(4π2r/T2)

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

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