The Inward Force AP Physics Centripetal Acceleration n

Centripetal Acceleration n Centripetal force and centripetal acceleration are always directed toward the center

Many Quantities n Velocity n Tangential (v) n Angular (ω) n Acceleration n Tangential

Total Linear Acceleration? n Tangential and centripetal acceleration are both linear quantities. n Always

Centripetal Force n Recall that according to Newton’s Second Law, the acceleration is directly

Centripetal Acceleration with angular quantities n Centripetal acceleration is always inward. n Must be

Centripetal Force is required for Circular Motion n As a car makes a turn,

Vertical Circular Motion n At the top of the motion: n At the bottom

Vertical Circle Practice n The maximum tension that a 0. 50 m string can

Friction and Centripetal Force Top view FN mg Side view Ff What is the

Forces on a Banked Curve Perfect Banking Going too fast n If the curve

Banked Incline n If a curve with a radius of 80 m is perfectly

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The Inward Force AP Physics

Centripetal Acceleration n Centripetal force and centripetal acceleration are always directed toward the center of the circular motion.

Many Quantities n Velocity n Tangential (v) n Angular (ω) n Acceleration n Tangential (a) n Angular (α) n Centripetal (a ) c Linear and angular quantities are related by the radius of revolution.

Total Linear Acceleration? n Tangential and centripetal acceleration are both linear quantities. n Always 90° apart. n There is a total linear acceleration as well. n Found by adding the two (tangential and centripetal) linear accelerations vectors together.

Centripetal Force n Recall that according to Newton’s Second Law, the acceleration is directly proportional to the Force. If this is true: Since the acceleration and the force are directly related, the force must ALSO point towards the center. This is called CENTRIPETAL FORCE. NOTE: The centripetal force is a NET FORCE. It could be represented by one or more forces. Do not draw on FBD.

Centripetal Acceleration with angular quantities n Centripetal acceleration is always inward. n Must be in units of kg·m/s² to get a force in Newtons

Centripetal Force is required for Circular Motion n As a car makes a turn, the force of friction acting upon the turned wheels of the car provide the centripetal force. n As a bucket of water is tied to a string and spun in a circle, the force of tension acting upon the bucket provides the centripetal force. n As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force.

Vertical Circular Motion n At the top of the motion: n At the bottom of the motion:

Vertical Circle Practice n The maximum tension that a 0. 50 m string can tolerate is 14 N. A 0. 25 kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed the ball can have: 1. 2. the top of the circle? at the bottom of the circle?

Answers n Top: n Bottom:

Friction and Centripetal Force Top view FN mg Side view Ff What is the minimum coefficient of static friction necessary to allow a penny to rotate along a 33 1/3 rpm record (diameter = 0. 300 m), when the penny is placed at the outer edge of the record?

Banked Curve n How is this possible?

Forces on a Banked Curve Perfect Banking Going too fast n If the curve is banked for n The car may begin to a perfect speed, there will be no slipping. n Normal component is inward. slide up the ramp. n Normal and friction components are inward. What about too slow?

Banked Incline n If a curve with a radius of 80 m is perfectly banked for a car traveling at 20 m/s, then what is the maximum safe speed for a car to not skid if the coefficient of static friction between the tires and the road is 0. 23. n First you must find the banking angle without friction. θ = 27° v = 25. 6 m/s