Question

A 210 g , 24-cm-diameter plastic disk is spun on an axle through its center by an electric motor.

Part A What torque must the motor supply to take the disk from 0 to 2000 rpm in 4.8 s ? Express your answer in newton-meters. τ τ = nothing   N⋅m

Answer 1

Mass of the disk = M = 210 g = 0.21 kg

Diameter of the disk = D = 24 cm = 0.24 m

Radius of the disk = R = D/2 = 0.24/2 = 0.12 m

Moment of inertia of the disk = I

I = MR²/2

I = (0.21)(0.12)²/2

I = 1.512 x 10^-3 kg.m²

Initial angular speed of the disk = ₁ = 0 rpm = 0 rad/s

Final angular speed of the disk = ₂ = 2000 rpm = 2000 x (2/60) rad/s = 209.44 rad/s

Time period = T = 4.8 sec

Angular acceleration of the disk =

₂ = ₁ + T

209.44 = 0 + (4.8)

= 43.633 rad/s²

Torque supplied by the motor =

I =

(1.512x10^-3)(43.633) =

= 6.6 x 10^-2 N.m

A) Torque supplied by the motor = 6.6 x 10^-2 N.m