Centripetal acceleration (12.2)

What is centripetal force?

Centripetal force - the resultant force towards the centre of a circle required to keep the body in uniform circular motion. It is always directed towards the centre of a body’s rotation.

Centripetal force is created by different forces depending on the situation:

What is centripetal acceleration and what causes it?

Centripetal acceleration - the acceleration of an object towards the centre of a circle when an object is in motion around a circle at a constant speed

Centripetal acceleration is caused by a centripetal force of constant magnitude.

Centripetal force and acceleration always act in the same direction.

A body in circular motion has a constantly changing direction so it has a constantly changing angular frequency. Therefore the body is always accelerating.

Centripetal acceleration causes circular motion with a constant angular speed

What are the three equations for centripetal acceleration?

a = vω = rω² = v²/r

Where a is centripetal acceleration (ms^-2)

Where v is linear speed (ms^-1)

Where ω is angular speed (radss^-1)

Where r is radius of the circle (m)

a = rω² can be derived from a = vω and v = rω:

a = (rω)ω = rω²

What are the equations for centripetal force?

F = ma = mvω = rω²m = (mv²)/r

Where F is centripetal force (N)

Where m is mass (kg)

Where a is centripetal acceleration (ms^-2)

Where v is linear speed (ms^-1)

Where ω is angular speed (radss^-1)

Where r is radius of the circle (m)