P$10\mathrm{.}14$ The torque exerted on the crankshaft of an engine is given by $(20,000+1500sin2-1320cos2)N-m.$ For a constant load torque, determine

$($a$)$ the average power of the engine operating at $1000$ rpm

$($b$)$ the mass of a $1\mathrm{.}2-$m$-$diameter solid disc flywheel so that the speed variation is less than $0\mathrm{.}3$ percent about the mean

$($c$)$ the rotational acceleration of the flywheel when $=45$