The rotor of an electric motor has a mass of 26 kg, and it is observed that 4.2 min is required for the rotor to coast to rest from an angular velocity of 3600 rpm. Knowing that kinetic friction produces a couple of magnitude 1.2 N·m, determine the centroidal radius of gyration for the rotor. (Round the final answer to one decimal place.)

0.2 m

Explanation:

m = mass of the rotor of an electric motor = 26 kg

R = radius of gyration = ?

magnitude of moment of inertia is given as

I = m R²

w₀ = initial angular velocity for rotor = 0 rad/s

w = final angular velocity of rotor = 3600 rpm = (3600) (2π/60) = 376.8 rad/s

t = time interval = 4.2 min = 4.2 x 60 sec = 252 sec

α = angular acceleration of rotor

Using the equation

w = w₀ + α t

376.8 = 0 + α (252)

α = 1.5 rad/s²

τ = magnitude of couple = 1.2 N-m

magnitude of couple is given as

τ = I α

τ = m R² α

1.2 = (26) (1.5) R²

R = 0.2 m