How does kinetic energy change in circular motion?

In summary, the kinetic energy of a body moving in a circle is dependent on its mass and velocity. If the circle is in a horizontal plane, the KE will not change. However, if the circle is in a vertical plane, the gravitational potential energy at the top will be 2mgr (where r is the radius) and zero at the bottom, causing the KE to vary in an opposite manner. This results in a constant total energy throughout the rotation. However, if the object is being forced to rotate at a constant speed, the KE will not change.
  • #1
Tangeton
62
0
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
 
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  • #2
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.
 
  • #3
Tangeton said:
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.
 
  • #4
Cool thanks for both answers.
 
  • #5
sophiecentaur said:
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.
 
  • #6
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.
 
Last edited:

FAQ: How does kinetic energy change in circular motion?

1. How does kinetic energy change in circular motion?

In circular motion, kinetic energy remains constant. This is because kinetic energy is defined as the energy an object possesses due to its motion, and the speed of an object moving in a circular path is constant. Therefore, the kinetic energy of an object in circular motion does not change.

2. Does the mass of an object affect its kinetic energy in circular motion?

No, the mass of an object does not affect its kinetic energy in circular motion. Kinetic energy is dependent on the speed of an object, not its mass. Therefore, regardless of the mass of an object, its kinetic energy will remain constant in circular motion.

3. How is kinetic energy calculated in circular motion?

Kinetic energy in circular motion can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its speed. However, since speed remains constant in circular motion, the kinetic energy can also be calculated as KE = 1/2 * m * r^2 * ω^2, where r is the radius of the circular path and ω is the angular velocity.

4. Can kinetic energy be converted into potential energy in circular motion?

No, kinetic energy cannot be converted into potential energy in circular motion. In order for energy to be converted from one form to another, work must be done. In circular motion, the force is always perpendicular to the displacement, so no work is done and thus, kinetic energy cannot be converted into potential energy.

5. How does the radius of the circular path affect kinetic energy?

The radius of the circular path does not affect kinetic energy. As mentioned earlier, kinetic energy in circular motion is dependent on the speed and not the radius. However, a larger radius may require a higher speed to maintain the circular motion, resulting in a higher kinetic energy due to the increased speed.

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