A microwave oven has a \(30-\mathrm{cm}\)-diameter rotating plate for even cooking. The plate accelerates from rest at a uniform rate of \(0.87 \mathrm{rad} / \mathrm{s}^{2}\) for \(0.50 \mathrm{~s}\) before reaching its constant operational speed.

(a) How many revolutions does the plate make before reaching its operational speed?

(b) What are the operational angular speed of the plate and the operational tangential speed at its rim?
THINKING IT THROUGH. This Example involves the use of the angular kinematic equations (Table 7.2). In (a), the angular distance \(\theta\) will give the number of revolutions. For (b), first find \(v\) and then \(v=r \omega\).

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TABLE 7.2 Equations for Linear and Angular Motion with Constant Acceleration" Linear Angular x= vt 0=cot (1) @+wo (2) @= 2 v=v+at x=x+vot+at v = v+2a (x-x) w=w+at 0=0+wt+at w=w+2a (0-6) 2 (3) (4) (5)