![]() Rotating objects have rotational kinetic energy, given by: (Notice these are the same as the original SUVAT equations, with the symbols replaced:Īny values with a subscript 0 mean that this is the initial, eg θ 0 is the initial angular displacement. If angular acceleration is constant, angular versions of the SUVAT equations can be used. Some of the above equations also need to be derived:īy differentiating, we get the relationship between speed and angular speed:Īnd similarly for acceleration and angular acceleration: If the object is not rotating at constant speed there is also a tangential force (at right angles to the radial component), causing it to accelerate. This is often provided by tension in a piece of string, friction between a road and tyres, or gravity.įorces in circular motion can be determined using the diagrams shown in forces. This is the centripetal force, which acts towards the centre of the circle (this is called a radial force). Speed is constant, but since the direction is changing the object is accelerating towards the centre of the circle.Īcceleration must be caused by a force, since F = ma. If kinetic friction does no work, ie the object is rolling without slipping: These are related by:Īngular displacement can therefore be written in two ways:Īngular speed, ω (greek letter omega), is the angular displacement per second. T is the period (the time for one complete circle) and f is the frequency. c is the circumference of the circle and r is the radius. An object is in uniform circular motion when it rotates at a steady rate.Īngular displacement, θ (greek letter theta), is the angle traveled by an object in time, t. ![]()
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