Rotation 1

Rotation 1

1. For given disc

   • Rotates about a perp axis
   • Rigid Body: So two points remain the same
   • All points rotate at same angle

2. Angular displacement

   • d@ = ds/r
     • @ in radians
     • one complete rev; @ = 2(pi)r / r
   • Each variable changes but ratio is the same
   • Measure in counter-clockwise

3. Angular Velocity

   • Time rate of change of angle is the same for all particles
   • Average; w = @/t
   • instantaneous; dw = d@/dt

4. angular acceleration

   • a = dw/dt = d^2@/dt^2
   • w=at

5. Rotation equation same as linear equation except

   • @ = x
   • w = v

6. Tangental(linear)

   • v(t) = rw = ds/dt = rd@/dt =
   • a(t) = dv/dt = rdw/dt = r~
     • ~ = angular acc

7. Centripetal acc

   • a = v^2/r
     • a = w^2r
   • Uniform motion = Const tang speed and a(t) = 0
     • Non-uniform = +/- tan speed
   • When r is different: w = same, v = outer, a(c) = outer