Circular Circular MotionMotion

Physics 1

What is “circular What is “circular motion”?motion”?

An object that moves in a circular path about an external point is in circular motion.

Angular VelocityAngular VelocityAn object in circular motion moves with an angular velocity () expressed in radians per second.

Tangential SpeedTangential SpeedAt any point in the circular path, the object has a linear (tangential) speed (vT ).

vT

The Value of vThe Value of vTT

The tangential speed depends on the size of the path circumference.

vT

vT

The Value of vThe Value of vTT

A larger path circumference means a larger path radius (r).

vT

vT

r

r

The Value of vThe Value of vTT

Tangential speed is directly proportional to the path radius.

Tv r

vT

vT

r

r

The Change in vThe Change in vTT

As an object moves between points in a circular path, the direction of vT changes. So, there is a v.

v1

v2 r

r

The Change in vThe Change in vTT

To find the direction of v, find the vector sum of v2 – v1.

The change in vT is directed toward the center of the circular path.

v1

v2

r -v1

v

The Change in vThe Change in vTT

Since there is a change in velocity, the object is undergoing an acceleration toward the center (centripetal). This is called centripetal acceleration (ac ).

The Value of aThe Value of acc

To find the magnitude of ac, use the two triangles formed in the diagram to the right.

v s

r

v1

v2

-v1

The Value of aThe Value of acc

Since the two triangles are similar,

v2

v1

s

r r

v

r

v

s

v T

The Value of aThe Value of acc

With vT being uniform in magnitude, s = vT t .

r

v

tv

v T

T

The Value of aThe Value of acc

Rearranging and simplifying,

r

vv

t

v TT

r

va Tc

2

Centripetal ForceCentripetal ForceFor circular motion, the net force influencing acceleration is called a centripetal force (Fc ).

v1

v2

r Fc

Fc

Centripetal ForceCentripetal ForceUsing Newton’s Second Law equation (Fnet = ma),

r

mvF Tc

2

cc maF