Determine the angular acceleration of the pulley of Figure 1.17.
Chapter 1
Q. 1.5
Step-by-Step
Verified Solution
Consider the system of rigid bodies composed of the pulley and the two blocks. If \alpha is the counterclockwise angular acceleration of the pulley, then, assuming no slip between the pulley and the cables, block A has a downward acceleration of r_{A}\alpha and block B has an upward acceleration of r_{B}\alpha.
Summing moments about the center of the pulley, neglecting axle friction in the pulley, and using the free-body diagrams of Figure 1.17(b) assuming moments are positive counterclockwise yields
\sum{M_{\omicron _{ext} } } =\sum{M_{\omicron _{eff} } }m_{A}gr_{A} – m_{B}gr_{B}= I_{P} \alpha +m_{B}r^{2}_{A}\alpha +m_{B}r^{2}_{B}\alpha
Substituting given values leads to \alpha =7.55 rad/ s^{2}.
