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ANGULAR MOTION

1 = ∏ / 180 rad

1 rad = 180/∏ = 57.3

Arc length (m):  S = r. θ

Δt:  Change in time (s)

 

LINEAR MOTION

ANGULAR MOTION

 

 

 

r:  Radius (m)

 

Δd:  Displacement (m)

 

Change in angular position (rad): Δθ  = Δd/r

 

v:  Tangential velocity (linear velocity) (m/s)

 

Angular velocity (rad/s):  w = v/r

                                or      w = Δθ / Δt

a:  Acceleration (m/s2)

 

Angular accelerating (rad/s2):  α = a/r

  

a = (v1 - v2) / Δt

 

α = Δw/ Δt = (w2 w1) / Δt

 

v2 = v1 + a Δt

 

w2 = w1 + α Δt

 

Δd = (v1 + v2) Δt

 

Δθ = (w1 + w2) Δt

 

Δd = v1. Δt + a Δt2

 

Δθ = w1. Δt + α Δt2

 

Δd = v2. Δt - a Δt2

 

Δθ = w2. Δt - α Δt2

 

v22 = v12 + 2a Δd

 

w22 = w12 + 2 α Δd

 

Centripetal acceleration (m/s2): ac = v2/r

 

Centripetal acceleration (m/s2): ac = (rw)2/r = rw2