Circular Motion: Angles & Velocity

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Angle

Angles can be measured in either degrees or radians

When dealing with circular motion, angles are always in radians.

2π radians = 360 º

Scalar quantity

θ = s/r

θ = angle in radians

s = arc length

r = radius

Angular Velocity

Symbol = ω

The rate of change of angle

Unit = radians per second

ω = θ/t

θ = angle in radians

t = time

Linear Velocity

Symbol = v

The speed of a particle in a direction perpendicular to the radius at that point

Vector quantity

Unit = metres per second

Relationship between angular velocity & linear velocity

Derivation:

v = s/t ... (definition of linear speed)

s = θr ... (definition of angle)

v = θr/t ... (combining the two equations)

ω = θ/t ... (definition of angular velocity)

v = θr/t ... (combining the two equations)

v = rω ... (subbing in ω for θ/t)

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