Notes
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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- Description
- This note covers angles & the two types of velocity in circular motion: angular velocity & linear velocity. This is best used alongside the mind map on circular motion. It is aimed at a leaving certificate student or someone who has an interest in circular motion.
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