Question

If the hoisting gear A has an initial angular velocity ωS = 8 rad/s and an angular deceleration αA = —1.5 rad/s². determine the velocity and acceleration of block C in 2 s.

Answer 1

The gear ratio is 2:1, meaning that two complete turns of the smaller gear equals one complete turn of the greater gear. Therefore, the initial angular velocity of the second gear is 4 rad/s. The final angular velocity of the greater gear B is

$$\omega_{Bf}=\omega_{Bi}+\alpha t,\\ \omega_{Bf}=4-1.5·2=1\text{ rad/s}^2.\\$$

The velocity and acceleration of block C in 2 s is

$$v_b=\omega_{Bf}r=0.05\text{ m/s}.\\ a_b=\omega^2_{Bf}r=0.05\text{ m/s}^2.$$