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PHYS 106 Chapter Notes -Circular Motion, Angular Velocity, Angular Acceleration

Course Code
PHYS 106
Alastair B Mc Lean

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Uniform circular motion
- motion at a constant SPEED around a circle
- in other words, the velocity vector is always equal in magnitude, and always tangent to the circle
Period (T): the time it takes for an object to make one revolution, in seconds. Eg. for 250 rps, T=1/250
Thus for uniform circular motion: |v|= 2πr/T
(circumference of a circle over time)
Angular position
- we can describe the position of a particle in circular motion by the radius of the circle and the angle it
makes counterclockwise from the x-axis
- relationship between arc length, angle, and radius:
s= θr
where r is in radians.
180* = π
Use this to convert between degrees and radians.
Angular displacement Δθ and angular velocity ω
- the change in a particle's position in circular motion can be measured by finding the change in its angle,
Δθ: the angular displacement
- the average change in a particle's angular displacement over time, is Δθ/Δt
Average angular velocity: Δθ/Δt
Taking the limit as t-> 0 gives the:
Instantaneous angular velocity: ω= dθ/dt, in rad/s
- this is the rate at which a particle's ANGULAR position is changing as it moves around the circle
- uniform circular motion can also now be defined as motion that has constant angular velosity
- counterclockwise = positive direction
The area (ω Δt) under the ω vs t curve, between t1 and t2 is θ12
Thus θ12= ω Δt
θ2= θ1+ ω Δt
Notice that all these equations parallel the definitions of displacement and velocity in non-accelerating
linear motion: D=vt
x12= v Δt
x2= x1 + vΔt
When the angular acceleration is constant/ 0, you can just use the constant acceleration kinematic
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