An lp turntable must spin at 3.500 rad/s to play a record. how much torque must the motor deliver if the turntable is to reach its final angular speed in 1.800 revolutions, starting from rest? the turntable is a uniform disk of diameter 30.80 cm and mass 0.2500 kg.

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".