# 14.2.2 Calculating Centripetal Acceleration

### Calculating Centripetal Acceleration

• Centripetal acceleration can be defined using the radius r and linear speed v:

• Using the equation relating angular speed ω and linear speed v:

v = r⍵

• These equations can be combined to give us another form of the centripetal acceleration equation:

• This equation tells us centripetal acceleration is equal to the radius times the square of the angular speed
• Alternatively, rearrange for r:

• This equation can be combined with the first one to give us another form of the centripetal acceleration equation:

• This equation tells us centripetal acceleration is equal to the linear speed times the angular speed

Centripetal acceleration is always directed toward the centre of the circle, and is perpendicular to the object’s velocity

• Where:
• a = centripetal acceleration (m s-2)
• v = linear speed (m s-1)
• ⍵ = angular speed (rad s-1)
• r = radius of the orbit (m)

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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