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An object of mass $m$ moves in a circle of radius $r$ - AQA - A-Level Physics - Question 28 - 2019 - Paper 1

Question 28

An object of mass $m$ moves in a circle of radius $r$. It completes $n$ revolutions every second. What is the kinetic energy of the object?

Worked Solution & Example Answer:An object of mass $m$ moves in a circle of radius $r$ - AQA - A-Level Physics - Question 28 - 2019 - Paper 1

Step 1

Determine the Angular Velocity

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Answer

The angular velocity $heta$ in radians per second is given by: $heta = 2\pi n$ where $n$ is the number of revolutions per second.

Step 2

Find the Linear Velocity

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Answer

The linear velocity $v$ of the object can be calculated from the angular velocity by the formula: $v = r\theta$ Substituting for $heta$ gives: $v = r(2\pi n) = 2\pi nr$ .

Step 3

Calculate the Kinetic Energy

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Answer

The kinetic energy (KE) of the object is given by the formula: $KE = \frac{1}{2} mv^2$ . Substituting the expression for $v$ : $KE = \frac{1}{2} m (2\pi nr)^2 = 2\pi^2 m n^2 r^2.$

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