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AQA A-level Physics Periodic motion

Periodic motion

This page covers the following topics:

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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Explain how it is possible that an object moving in a circle at a constant speed has a changing velocity.

AQA A-level Physics Periodic motion Explain how it is possible that an object moving in a circle at a constant speed has a changing velocity.
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A yo-yo is being made to move in circular motion in a circle of radius 1.2 m. Calculate the angular displacement of the yo-yo when it moves through an arclength of 80 cm.

AQA A-level Physics Periodic motion A yo-yo is being made to move in circular motion in a circle of radius 1.2 m. Calculate the angular displacement of the yo-yo when it moves through an arclength of 80 cm.
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3

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A runner runs 4 circular laps in 5 minutes. What is the angular speed of the runner?

AQA A-level Physics Periodic motion A runner runs 4 circular laps in 5 minutes. What is the angular speed of the runner?
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4

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Given that the velocity of a runner running on a circular track of radius 22 m is 5 m/s, calculate the angular displacement of the runner in 38 seconds to 3 significant figures.

AQA A-level Physics Periodic motion Given that the velocity of a runner running on a circular track of radius 22 m is 5 m/s, calculate the angular displacement of the runner in 38 seconds to 3 significant figures.
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5

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What is the centripetal acceleration of an object moving in a circle of radius 20 m at a velocity of 12 m/s?

AQA A-level Physics Periodic motion What is the centripetal acceleration of an object moving in a circle of radius 20 m at a velocity of 12 m/s?
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6

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The centripetal acceleration of a skater is 4.5 m/sΒ². Given that she is skating around in a circle of radius 5 m, calculate the velocity of the skater.

AQA A-level Physics Periodic motion The centripetal acceleration of a skater is 4.5 m/sΒ². Given that she is skating around in a circle of radius 5 m, calculate the velocity of the skater.
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7

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State the conditions which are required for an object to be oscillating with simple harmonic motion.

AQA A-level Physics Periodic motion State the conditions which are required for an object to be oscillating with simple harmonic motion.
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8

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Explain which of the given diagrams correctly represents a suspended object moving in simple harmonic motion.

AQA A-level Physics Periodic motion Explain which of the given diagrams correctly represents a suspended object moving in simple harmonic motion.
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9

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Given that an object is oscillating in simple harmonic motion at a frequency of 4.2 Hz, calculate the distance of the object from the equilibrium position when its acceleration is 40 m/sΒ².

AQA A-level Physics Periodic motion Given that an object is oscillating in simple harmonic motion at a frequency of 4.2 Hz, calculate the distance of the object from the equilibrium position when its acceleration is 40 m/sΒ².
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10

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At which part of its oscillation does an object moving in simple harmonic motion have maximum acceleration?

AQA A-level Physics Periodic motion At which part of its oscillation does an object moving in simple harmonic motion have maximum acceleration?
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11

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Given that the amplitude of a ball's oscillation is 30 cm and that its maximum speed is 7 m/s, calculate the frequency at which it is oscillating.

AQA A-level Physics Periodic motion Given that the amplitude of a ball's oscillation is 30 cm and that its maximum speed is 7 m/s, calculate the frequency at which it is oscillating.
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12

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What is the maximum velocity reached by a ball attached to a spring oscillating at 2 Hz with amplitude of 3 cm?

AQA A-level Physics Periodic motion What is the maximum velocity reached by a ball attached to a spring oscillating at 2 Hz with amplitude of 3 cm?
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