Centripetal Force
To give an object moving in a circle the centripetal acceleration needed to keep moving, it needs a force applied to it. Any force that causes an object to move in a circle is a centripetal force. Gravity, tension, friction, and other forces can all act as centripetal forces; all of these forces can act to pull or push an object into a circle.
Because F = ma, the centripetal force F_{c} is just ma_{c}. Here’s the equation for centripetal force:
You can also calculate the centripetal acceleration a_{c} using the angular velocity:
This means that you can also calculate the centripetal force with the following formula:
Sample question

The moon goes around Earth about every 27.3 days with a distance from Earth of 3.85 x 10^{8} m. If the moon’s mass is 7.35 x 10^{22} kg, what is the centripetal force that Earth’s gravity exerts on it as it orbits Earth?
The correct answer is 2.0 x 10^{20} N.

Start with this equation:

Find the speed of the moon. It goes 2ðr in 27.3 days, so convert 27.3 to seconds:

Therefore, the speed of the moon is

Plug in the numbers:

Practice questions

You’re exerting a force on a string to keep a ball on a string going in a circle. If the ball has a mass of 0.10 kg and the angular velocity of the ball is 8.0 radians/s at a distance of 2.0 m, what is the centripetal force you need to apply to keep the ball going in a circle?

You have a 1.0kg toy plane on the end of a 10m wire, and it’s going around at 6.0 radians/s. What is the force you have to apply to the wire to keep the plane going in a circle?
Following are answers to the practice questions:

13 N

Use the equation for a centripetal force:

Plug in the numbers:


360 N

Use this equation for a centripetal force:

Plug in the numbers:
