# We also saw in general d l dt therefore z dl z dt di

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We also saw, in general ~ = d ~ L dt Therefore z = dL z dt = dI ! dt = I d ! dt = I This is nothing but Newton’s second law or rigid body motion with fixed axis of rotation!

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Phys 2A - Mechanics Parallel Between Translational and Rotational Motion x, v = dx dt , a = d 2 x dt 2 , = d dt , α = d 2 dt 2 = α t + 0 = 1 2 α t 2 + 0 t + 0 2 = 2 0 + 2 α ( - 0 ) α = constant v = at + v 0 x = 1 2 at 2 + v 0 t + x 0 v 2 = v 2 0 + 2 a ( x - x 0 ) a = constant F, p, m τ , L, I F net = dP dt τ net = d L dt L z = I ω P = MV CM K = 1 2 mv 2 K = 1 2 I ω 2 W = d θ , dW dt = ⇥⇤ W = F x dx, dW dt = F x v x
Phys 2A - Mechanics Gyroscope x y v x v y ~ v ~ a p x p y ~ F ~ p d ~ v dt = ~ a with ~ a ? ~ v d ~ p dt = ~ F with ~ F ? ~ p d ~ L dt = ~ with ~ ? ~ L ) ) ) L x L y ~ L ~ ~ W ~ ~ L ( ~ into the slide)

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Phys 2A - Mechanics Kepler’s Laws Will be presented in DI. The third one is more general than just for planets. In particle motion, if L is conserved then (i) the particle moves in a fixed plane and (ii) the angle swept by the particle per unit time is constant Proof: (i) The motion is in the plane perpendicular to L (ii) In that plane ~ r ~ vdt v ? dt dA = 1 2 | ~ r | v ? dt or dA dt = 1 2 | ~ r ~ v | = 1 2 m | ~ L |
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