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Periodic motion

Periodic motion

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A body moving around in a circle at a constant speed is accelerating, since its direction and thus its velocity are changing. According to Newton's Second Law, a force must be acting on the body. For the speed to be constant, the force must be perpendicular to the speed and direction of modion, which is tangential to the path. Therefore, there is a resultant force called the centripetal force acting towards the centre of the circle, along its radius and the object is said to be in circular motion.

Circular motion

For an object travelling in circular motion, the angular displacement is the angle covered by the body in radians and it is calculated using the formula ΞΈ = arc/radius. The angular displacement can then be used to find the angular speed of an object using the formula Ο‰ = ΞΈ/t. Angular speed is given in rad/s.

Angular speed

An object moving in circular motion is accelerating since it has a changing velocity. This is because of the fact that the direction of the object is changing since it is moving in a circle. Centripetal acceleration can be caluclated using the following formula: a = vΒ²/r = ω²r.

Centripetal acceleration

Simple harmonic motion is a type of oscillation that only occurs when the following two conditions are met. Firstly, the acceleration of the object must be directly proportional to its displacement from its equilibrium position and secondly, the acceleration must always be directed towards the equilibrium position. The magnitude of simple harmonic acceleration can be calculated using the following formula: acceleration = (2Ο€ Γ— frequency)Β² Γ— displacement.

Simple harmonic acceleration

An object oscillating in simple harmonic motion reaches maximum speed at the equilbrium position. In this position, the acceleration of the objetct is 0. At maximum amplitude, the object has a velocity of 0, however has a maximum acceleration. The maximum speed reached by the object can be calculated using the following formula: max. velocity = A Γ— 2Ο€f, where A = amplitude.

Maxima of simple harmonic motion

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