A2 Unit 12 Circular Motion

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Define radian

The angle subtended at the centre of a circle by an arc equal in length to the radius

Define angular velocity

The rate of change of angle by a object following a circular path/rotating

Relationship between angular speed and time period

ω = 2π/T

Relationship between angular speed and linear speed

ω = v/r

Define centripetal force

The force necessary to keep an object on a circular path. The direction is towards the centre of the circle.

Define centripetal acceleration

Property of an object following a circular path. The direction is towards the centre of the circle. The acceleration is due to the object constantly changing linear velocity due to changing direction

Relationship between centripetal acceleration and angular velocity

a = ω²r

Relationship between centripetal acceleration and linear speed

a = v²/r

Relationship between centripetal force and angular velocity

F = mω²r

Relationship between centripetal force and linear speed

F = mv²/r