84.5 The circular motion d0=o, dt=l(o,+a,t)dt 6(1)=6+0t+a Comparison: nonounoform circular motion with a constant angular acceleration and the rectilinear motion with a constant acceleration asdo2≠ costant dy dt costant o(t )=m0+a,t z0 v (t=vro +at 6(0)=6+0t+a:2(x()=x+vnt+,at 84.5 The circular motion Exercise 1 Your antique stereo turntable of radius 13.7 cm, initially spinning at 33.0 revolutions per minute is shut off. The turntable coasts to a stop after 120 s Assume a constant angular acceleration. Calculate the angular acceleration of the turntable and the number of revolutions through which it spins as it stops.18 2 0 0 0 0 0 2 1 ( ) d d ( )d 0 t t t t t t z z t z z t z θ θ ω α θ ω ω α θ θ = + + = = + ∫ ∫ ∫ costant d d = = t z z ω α 2 0 0 2 1 (t) t t θ = θ +ω z + α z t t ω z =ω z0 +α z ( ) costant d d = = t v a x x 2 0 0 2 1 x(t) x v t a t = + x + x v t v a t x = x0 + x ( ) Comparison : nonounoform circular motion with a constant angular acceleration and the rectilinear motion with a constant acceleration §4.5 The circular motion Exercise 1: Your antique stereo turntable of radius 13.7 cm, initially spinning at 33.0 revolutions per minute, is shut off. The turntable coasts to a stop after 120 s. Assume a constant angular acceleration. Calculate the angular acceleration of the turntable and the number of revolutions through which it spins as it stops. §4.5 The circular motion