Chapter 07b - Chapter 7B Tangential and Centripetal...

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Chapter 7B 1 Tangential and Centripetal Acceleration An object is accelerating whenever its velocity is changing. Velocity is a vector quantity, so it has a magnitude and a direction. An object is undergoing tangential acceleration ( a t ) if the magnitude of its velocity is changing (if it is speeding up, or slowing down). An object is undergoing centripetal acceleration ( a c ) if the direction of its velocity is changing (if it is traveling in a circular path).
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Chapter 7B 2 Tangential and Centripetal Acceleration • Tangential acceleration ( a t ) and centripetal acceleration ( a c ) are always perpendicular to each other. An object’s total acceleration ( a ) will be the vector sum of its tangential and centripetal accelerations: a = a t 2 + a c 2
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Chapter 7B 3 Centripetal Force When an object is traveling in a circular path at a constant speed it is accelerating toward the center of the circle. Newton’s Second Law tells us there must be a net force directed toward the center of the circle : F c = ma c F c = mv t 2 r
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Chapter 7B 4 Car Traveling Around Unbanked Curve The car’s front tires exert a sideways force on the road. The road exerts an equal but opposite sideways force on the front tires. The centripetal force F c is provided by the static friction between the tires and the road. F C
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Chapter 7B 5 Car Traveling Around Unbanked Curve The static frictional force that we need to negotiate the curve is: f s = F c = mv 2 r The maximum static frictional force that we can get is: f s ,max = μ s mg If the amount of static friction that we need is less
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Chapter 07b - Chapter 7B Tangential and Centripetal...

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