A flywheel of mass 192 kg has an effective radius of 0.620 m (assume that the mass is concentrated along a circumference located at the effective radius of the flywheel). What constant torque is required to bring the wheel from rest to an angular speed of 131 rev/min in a time interval of 30.0 s? 30.92 N⋅m

30.85 N-m

Explanation:

we can use the work energy theorem

that ΔK = 1/2Iω_f^2 - 1/2Iω_i^2

= 1/2mR_eff^2*ω_f^2-0

= 0.5*192*0.62^2*2π*120/60

=0.463

b) If the torque is constant then so is the angular acceleration. Hence, ω_f = ω_i+αt

now α = 4π/30 = 0.4180

then we use the relationship τ = Iα = to calculate the torque

τ = mr^2 (α)

τ = 192*0.62^2*0.4180

= 30.85 N-m