# How does kinetic energy change in circular motion?

Could someone explain to me how the kinetic energy of a body moving in a circle is like? I got tempted it stays constant as the speed is constant but that turned out to be false.

I am interested in places where the body is at top, side and bottom and so on. So I'd like to also know what the KE will be at those points...

Thank you

## Answers and Replies

sophiecentaur
Science Advisor
Gold Member
2020 Award
If the circle is in a horizontal plane then the KE will not change. If the circle is in a vertical plane then the gravitational potential at the top will be 2mgr (r is the radius) and zero at the bottom. The KE will vary in the opposite way - according to the gpe in any position, giving constant total energy throughout the rotation.

Could someone explain to me how the kinetic energy of a body moving in a circle is like? I got tempted it stays constant as the speed is constant but that turned out to be false.

I am interested in places where the body is at top, side and bottom and so on. So I'd like to also know what the KE will be at those points...

Thank you

Kinetic energy classically follows the following equation:
$$KE = \frac{1}{2}mv^2$$
Where m is mass, and v is velocity. Assuming it's vertical in a uniform gravitational field, the KE will be maximum at the bottom, and minimum at the top. At the left and right, it will be equal.

Cool thanks for both answers.

CWatters
Science Advisor
Homework Helper
Gold Member
If the circle is in a vertical plane then the gravitational potential at the top will be 2mgr (r is the radius) and zero at the bottom. The KE will vary in the opposite way - according to the gpe in any position, giving constant total energy throughout the rotation.

That assumes the object isn't being forced to rotate at a constant speed. For example a pendulum trades off PE vs KE as it rotates but a DVD in a vertical DVD player doesn't.

sophiecentaur
Science Advisor
Gold Member
2020 Award
True. Except that, by definition, the KE cannot change if the speed remains the same. But the OP didn't specify clearly enough - this will happen if one doesn't know the subject well. A common PF problem.

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