Uniform Circular Motion Circular Motion Uniform circular motion

Circular Motion Uniform circular motion occurs when an object travels in a circular path

Centripetal force Any acceleration must be caused by a force. In circular motion, centripetal

Circular Motion Calculations Centripetal acceleration is calculated using the formula… a = v 2

E. g. 1 A stone of mass 0. 5 kg on the end of

Vertical Circular Motion When moving at a constant speed in a vertical circle, the

A At A: The tension is smallest because part of the centripetal force is

Rollercoaster Physics Q. Consider the forces acting on a rollercoaster at the top and

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Uniform Circular Motion

Circular Motion Uniform circular motion occurs when an object travels in a circular path at a constant speed. Uniform circular motion acceleration Instantaneous velocity 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.

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

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

E. g. 1 A stone of mass 0. 5 kg on the end of a string 250 cm long is swung in a horizontal plane at a constant speed of 10 ms-1. What is the tension in the string? A. F = mv 2 r = 0. 5 x 102 2. 5 = 20 N

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

A 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. T mg D T B T T mg mg C mg At B and D: At A: The tension provides all of the centripetal force as the weight is perpendicular to the tension. mv 2/r = mg + T At C: mv 2/r = T – mg At B and D: mv 2/r = T

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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