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Uniform Circular Motion

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Circular Motion Uniform circular motion occurs when an object travels in a circular path at a constant speed. Uniform circular motion Instantaneous velocity acceleration Q. Explain why a ball moving in a circle must be accelerating towards the centre. A. - Magnitude of velocity is constant - Direction of velocity changes - Thus v is changing so it must be accelerating.

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Centripetal force Any acceleration must be caused by a force. In circular motion, centripetal acceleration is caused by the centripetal force (which acts towards the centre of the circle). v Centripetal force Q. Explain what provides the centripetal force upon the following objects moving in circular motion: a. A planet b. An electron c. A cornering cyclist d. A banking aircraft e. Wall of death motorcyclist f. The clothes in a spin drier

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Circular Motion Calculations Centripetal acceleration is calculated using the formula… Thus, using F = ma Note that using the speed formula we can say… where… a = v 2 r v = tangential velocity at any instant (ms -1 ) r = radius of circle (m) a = centripetal acceleration (ms -2 ) Centripetal force = mv 2 r v = 2πr T T = 1 f Q. What would be the effect of reducing the centripetal force for a car cornering at a fixed velocity?

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E.g.1 A stone of mass 0.5kg on the end of a string 250cm long is swung in a horizontal plane at a constant speed of 10ms -1. What is the tension in the string? A. F= mv 2 r = 0.5 x = 20N

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Vertical Circular Motion When moving at a constant speed in a vertical circle, the centripetal acceleration and centripetal force must both be constant. A D C B mg T TT T E.g. A bucket swinging vertically on a string:

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At A: The tension is smallest because part of the centripetal force is provided by the weight. At C: The tension is greatest because the tension must hold up the weight as well as supply the centripetal force. At B and D: The tension provides all of the centripetal force as the weight is perpendicular to the tension. A D C B mg T TT T At A: mv 2 /r = mg + T At C: mv 2 /r = T – mg At B and D: mv 2 /r = T

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Rollercoaster Physics Q. Consider the forces acting on a rollercoaster at the top and bottom of its motion. Can you write equations describing the centripetal force similar to the last example? B A

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