ObjectivesExplain why an object moving in a circle at a constant speed is accelerated.Describe how centripetal acceleration depends upon the object’s speed and the radius of the circle.Identify the force that causes centripetal acceleration.

INTROAcceleration deals with a change in

velocity (vector quantity thus magnitude and DIRECTION) divided by a change in time, thus something that is moving around in a circle at a constant speed has acceleration since the direction is changing.

DESCRIBING CIRCULAR MOTION Uniform Circular Motion – the movement of an object or particle

trajectory at a constant speed around a circle with a fixed radius.  v = Δd / Δt = Δr / Δt   Tangent – a straight line or plane that touches a curve or curved

surface at a point but does not intersect it at that point   As the velocity vector moves around the circle, its direction changes

but its length remains the same.

  a = Δv / Δt

Acceleration vector of an object in uniform circular motion always points toward the center of the circle. 

DESCRIBING CIRCULAR MOTIONCentripetal – a quantity that always points

toward the center of a circle; center seeking; it was originated by Sir Isaac Newton.

Centripetal Acceleration – the Center Seeking acceleration of an object moving in a circle at constant speed.

CENTRIPETAL ACCELERATIONCentripetal Acceleration – the Center Seeking

acceleration of an object moving in a circle at constant speed. It always points toward the center of the circle. Its magnitude is equal to the square of the speed divided by the radius of motion.

ac = v2 / r

 Period – the time needed for an object to make one

complete revolution. It is denoted by T. Velocity of an object traveling around a circle can

be found by v = 2Πr / T

CENTRIPETAL ACCELERATIONAnd because of that we can find the Acceleration

byac = 4Π2r / T2

 Centripetal Force – the net force exerted

toward the center of the circle that causes an object to have a centripetal acceleration. It is equal to the mass of the object times its centripetal acceleration.

Fc = mac

CENTRIPETAL ACCELERATIONDo Example Problem 2 p. 155

ac = 4Π2r / T2 Then FT = Fc = mac

ac = 4Π2(.93) / (1.18)2 FT = .013(26.34) ac = 36.68 / 1.3924 FT = .342 N ac = 26.34 m/s2

 Do Practice Problems p. 156 # 12-15

A NONEXISTENT FORCE Remember Newton’s First Law states that an

object at rest will stay at rest and an object in motion will stay in motion unless acted on by an outside force.

 Go over example of the car and turning. Centrifugal Force – an outward force. It is

fictitious. It does not exist.

Do 6.2 Section Review p. 156 # 16-21