This

**preview**shows page 1. to view the full**4 pages of the document.**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

equations:

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