Answer
29977.15 Rev
Work Step by Step
Find the final angular velocity (omega) and convert to radians.
15000 Rev/60 Sec = 250 Rev/Sec
250 × 2π = 1570.8 Rad/Sec
ω (initial) = 0 because it is starting from rest.
To find the angular acceleration (alpha), use the equation:
ω (final) = ω (initial) + α (alpha) t (time)
1570.8 = 240 sec × α (alpha)
Angular acceleration = 6.54 Rad/Sec$^{2}$
To find θ, use the equation:
θ = ω (initial) t + (1/2) α (alpha) t$^{2}$
θ = 0 + (1/2)(6.54)(240 sec)$^{2}$
θ = 188352 Rad
Rev = θ/(2π)
Rev = 188352 Rad/(2π) = 29977.15 Rev