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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 Q. Explain why a ball moving in a circle must be accelerating towards the centre. Instantaneous velocity acceleration 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). 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 v Centripetal force

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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 = v2 r v = tangential velocity at any instant (ms-1) r = radius of circle (m) a = centripetal acceleration (ms-2) Q. What would be the effect of reducing the centripetal force for a car cornering at a fixed velocity? Centripetal force = mv2 r v = 2πr T T = 1 f

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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 = mv2 r = 0.5 x 102 2.5 = 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 E.g. A bucket swinging vertically on a string: mg T T T mg mg T mg

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A D C B 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. mg T T T mg mg T mg At A: mv2/r = mg + T At C: mv2/r = T – mg At B and D: mv2/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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