CIRCULAR MOTION

WHAT IS UNIFORM CIRCULAR MOTION

•The motion of an object in a circle at constant speed.

•However, direction and therefore velocity are changing. This means the object is constantly accelerating toward the center.

•Example: a Ferris wheel•Any object that revolves about a single axis

(axis of rotation) undergoes circular motion•For the Ferris wheel the axis of rotation is

perpendicular to the side of the wheel and passes through the center

Looking closer

• Centripetal acceleration- the acceleration of an object in circular motion acting toward the center of the circle

• Centripetal Force - the force which acts on an object toward the center of the circle to produce centripetal acceleration

• Centrifugal Force - the equal and opposite reaction to centripetal force

EQUATION FOR CENTRIPETAL ACCELERATION

•Acceleration is acting toward the center

•Velocity is acting tangent to the circle

•The equation becomes –

•ac=vt2/r

•Where: ac is centripetal acceleration

• vt is tangential velocity

• r is the radius

EQUATION FOR CENTRIPETAL FORCE•The net force acting

on a circling object is perpendicular to its motion

•The equation becomes –

•Fc=mac•Fc is centripetal force•m is mass•ac is centripetal

acceleration

AN EXAMPLE

•An object with a mass of 5.0 kg moves in a circular path of radius 0.50 meters at a speed of 10. m/s. Calculate the centripetal acceleration and the centripetal force.

THE SOLUTION

•ac=vt2/r

• = (10. m/s)2/(.50 m)• = 2.0 x 102 m/s2

•Fc=mac

• =(5.0kg)(10.m/s)2/(.50m)• = 1.0 x 103 N