Objectives  Explain 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.

INTRO Acceleration 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 MOTION Centripetal – 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 ACCELERATION Centripetal 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. a c = v 2 / 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 ACCELERATION And because of that we can find the Acceleration by a c = 4Π 2 r / T 2 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. F c = ma c

CENTRIPETAL ACCELERATION Do Example Problem 2 p. 155 a c = 4Π 2 r / T 2 ThenF T = F c = ma c a c = 4Π 2 (.93) / (1.18) 2 F T =.013(26.34) a c = / F T =.342 N a c = m/s 2 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