The load \(L\) is being hoisted by the pulley-and-cable arrangement shown. Each cable is wrapped securely around its respective pulley so it does not slip. The two pulleys to which \(L\) is attached are fastened together to form a single rigid body. Calculate the velocity and acceleration of the load \(L\) and the corresponding angular velocity \(\omega\) and angular acceleration \(\alpha\) of the double pulley under the following conditions:

Case

(a) Pulley 1:

\(\omega_{1}=\dot{\omega}_{1}=0\) (pulley at rest)

Pulley 2: \(\quad \omega_{2}=2 \mathrm{rad} / \mathrm{sec}, \alpha_{2}=\dot{\omega}_{2}=-3 \mathrm{rad} / \mathrm{sec}^{2}\)

Case

(b) Pulley 1:

Pulley 2:

\(\omega_{1}=1 \mathrm{rad} / \mathrm{sec}, \alpha_{1}=\dot{\omega}_{1}=4 \mathrm{rad} / \mathrm{sec}^{2}\)

\(\omega_{2}=2 \mathrm{rad} / \mathrm{sec}, \alpha_{2}=\dot{\omega}_{2}=-2 \mathrm{rad} / \mathrm{sec}^{2}\)

Transcribed Image Text:

"14" 1 001 4" -12=4" D W2 At B L 8"