C IRCULAR M OTION Section 6.2 Pg

O BJECTIVES Explain why an object moving in a circle at constant speed is accelerating. Describe how centripetal acceleration depends upon the object’s speed and the radius of the circle. Identify the force that causes the centripetal acceleration Explain the “nonexistent Force” (inertia)

U NIFORM C IRCULAR M OTION Movement of an object around a circle of fixed radius at constant speed Question: Why does it state constant speed instead of constant velocity? Notice the direction of velocity is different at different points in the circle; thus velocity is NOT constant.

V ELOCITY AROUND A CIRCLE Since direction is constantly changing, we look only at the magnitude of the velocity (speed) Distance around a circle is called the CIRCUMFERENCE. Time taken to go around the circle once is called PERIOD. v = velocity (m/s) r = radius (m) T = period (s)

U NIFORM C IRCULAR M OTION At any given point, velocity is always tangent to the circle. Therefore, velocity is always changing An object that is changing its velocity must be experiencing an acceleration. Accelerations are caused by forces, therefore, there must be a force acting on the object in order to keep it going in a circle. Think back to the bowling ball lab!! What did you need to do to the ball to keep it going around in a circle?

C ENTRIPETAL ACCELERATION Centripetal Acceleration Direction: Always points to the center of the circle Magnitude: related to the velocity squared and inversely related to the radius of the circle. Centripetal acceleration and velocity are always perpendicular to each other. a c = centripetal acceleration (m/s 2 ) v = velocity (m/s) r = radius (m) Since you needed to apply a force towards the center of the circle in the bowling ball lab, the acceleration must also point towards the center of the circle.

C ENTRIPETAL FORCE Newton’s Second Law gets rewritten as the net centripetal force is equal to the mass of the object times the centripetal acceleration of the object. F c = Centripetal Force (N) ac = centripetal acceleration (m/s2) m = mass (kg) Describes the net force toward the center of the circle. It is NOT a type of force, but in actuality, describing how a force is acting.

C ENTRIPETAL F ORCES Lets take a look at a Ferris wheel and draw a FBD at four points: TOP FgFg FgFg FNFN FNFN acac TOP Normal force points up (-) Weight points down (+) Centripetal acceleration points into the circle (DOWN) Therefore, the weight force must be greater than the normal force up. You feel LIGHTER at the top of the Ferris wheel

C ENTRIPETAL F ORCES Lets take a look at a Ferris wheel and draw a FBD at four points: BOTTOM FgFg FgFg FNFN acac acac BOTTOM Normal force points up (+) Weight points down (-) Centripetal acceleration points into the circle (UP) Therefore, the normal force up must be greater than the weight force down. You feel HEAVIER at the bottom of the Ferris wheel

C ENTRIPETAL F ORCES Lets take a look at a Ferris wheel and draw a FBD at four points: SIDES FgFg FNFN acac SIDES Normal force points up Weight points down Centripetal acceleration points into the circle (LEFT/RIGHT) Therefore, neither the normal force nor the weight force act centripetally. Vertically in equilibrium – normal force must be equal to weight force. You feel YOUR TRUE WEIGHT at the sides of the Ferris wheel FgFg FNFN acac

C ENTRIPETAL F ORCE What forces can be seen acting centripetally? 1. Gravitational Force (vertical circles) 2. Normal Force (Gravitron, Ferris Wheel) 3. Tension (String) 4. Friction (Horizontal circle- car around turn)

C ENTRIPETAL F ORCES - FBD Centripetal motion can be identified more specifically as vertical circular motion or horizontal circular motion. HORIZONTALVERTICAL Examples: Car around a turn, gravitron, twirling a ball around in a circle Examples: Ferris wheel, air show of jets doing nose dives Draw the FBD as a top viewDraw the FBD as a side view ONLY forces that point directly into the circle or directly out of the circle act centripetally. Forces pointing into the circle – POSITIVE Forces pointing out of the circle - NEGATIVE

N ON - EXISTENT FORCE Take a car making a sharp right turn A passenger in the car is going to feel like they are being “pushed” towards the left (outward from the turn). Question: Is there a force that is pushing the passenger to the left when the car is making a right turn? There is no outward force acting on you, it is your body’s inertia (resistance to change) that keeps your body from following the car through the turn. NEWTON’S FIRST LAW – object in motion stays in motion in a straight line at constant velocity unless acted on by a net force.

C ENTRIPETAL F ORCE Q UESTION What happens if the centripetal force stops existing? Does the object continue in a circular path? If the centripetal force stops existing, then Newton’s First Law explains that the object will continue in a straight line at constant velocity until it encounters another force.