Circular Motion: Angles & Velocity

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 velocityDerivation: 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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