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Centripetal Acceleration

Objects moving in a circle must experience acceleration and force perpendicular to their direction of travel.

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Centripetal Acceleration

Students will learn what centripetal acceleration is, where it applies and how to calculate it. Students will also learn when a force is acting as a centripetal force and how to apply it.

Key Equations

Centripetal Force

FC=mv2rmvrmass (in kilograms, kg)speed (in meters per second, m/s)radius of circle

Centripetal Acceleration

aC=v2r{vrspeed (in meters per second, m/s)radius of circle

Guidance

If a mass m is traveling with velocity v and experiences a centripetal --- always perpendicular --- force Fc, it will travel in a circle of radius

Undefined control sequence \intertext

Example 1

If you are 4m from the center of a Merry-Go-Round that is rotating at 1 revolution every 2 seconds, what is your centripetal acceleration?

Solution

First we need to find your tangential velocity. We can do this using the given angular velocity.

ωωωvvv=2π rad2 s=π rad/s=vr=ωr=πrad/s4m=4πm/s

Now we can find your centripetal acceleration using the radius of your rotation.

acacac=v2r=(4πm/s)24m=4π2m/s2

Watch this explanation

Simulation

Ladybug Motion in 2D (PhET Simulation)

Time for Practice

  1. A 6000 kg roller coaster goes around a loop of radius 30m at 6 m/s. What is the centripetal acceleration?
  2. For the Gravitron ride above, assume it has a radius of 18 m and a centripetal acceleration of 32 m/s2. Assume a person is in the graviton with 180 cm height and 80 kg of mass. What is the speed it is spinning at? Note you may not need all the information here to solve the problem.

Answers

1. 1.2 m/s2

2. 24 m/s

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