Physics 1A, Section 2 November 11, 2010

Translation / Rotation translational motionrotational motion position x angular position  velocity v = dx/dt angular velocity  = d  /dt acceleration a = dv/dt = d 2 x/dt 2 angular acceleration  = d  /dt = d 2  /dt 2 mass mmoment of inertia I momentum p = mv angular momentum L = I  force F = ma torque  = I  kinetic energy ½ mv 2 kinetic energy ½ I  2

Quiz Problem 25

Answer: a) T = a(mR 2 + I )/[R(R-r)] f = a( I + mrR)/[R(R-r)] b)  min = a(kR + r)/[g(R-r)] c) rolls to the right

Moment of Inertia Moments:  0 th moment: ∫dm = mass  useful 1 st moment: ∫ r dm 1/M ∫ r dm is the center of mass  useful 2 nd moment: ∫R 2 dm = moment of inertia  R is the distance from the axis of rotation  Other ways to write the integral: ∫dm = ∫  dV = ∫∫∫  dx dy dz Moment of inertia examples: Frautschi et al. Table 14.1, page 379 Parallel axis theorem: I = I CM + Md 2

Quiz Problem 41

Answer: a)  1 = 8  da 4  2 = ½  da 4  1 /  2 = 16 b)  f = 16  /17 c) No, some lost to friction. K final /K initial = 16/17

Quiz Problem 32 (collision with rotation) Optional, but helpful, to try these in advance. Monday, November 15: