Halliday, Resnick & Walker — Rotation: Problem Problem_74

Racing disks. Figure 10.32 shows two disks that can rotate about their centers like a merry-go-round. At time \( t = 0 \), the reference lines of the two disks have the same orientation. Disk A is already rotating, with a constant angular velocity of \( 9.5 \text{ rad/s} \). Disk B has been stationary but now begins to rotate at a constant angular acceleration of \( 2.2 \text{ rad/s}^2 \). (a) At what time \( t \) will the reference lines of the two disks momentarily have the same angular displacement \( \theta \)? (b) Will that time \( t \) be the first time since \( t = 0 \) that the reference lines are momentarily aligned?