Question

While spinning down from 500.0 rpm to rest, a solid uniform flywheel (Disk) does 2.3 kJ of work. If the radius of the disk is 1.2 m, what is its mass? A) 3.0 kg B) 2.3 kg C) 2.6 kg D) 2.0 kg

Answer 1

Option (B)

Step-by-step explanation:

Let m be the mass of solid disc.

initial frequency, fo = 500 rpm = 8.33 rps

initial angular velocity, ωo = 2 x 3.14 x 8.33 = 52.33 rad/s

final angular velocity, ω = 0 rad/s

Work done = change in kinetic energy

Let I be the moment of inertia of the disc

Initial kinetic energy

`K_(1)=0.5 * I * \omega ^(2)`

`K_(1)=0.5 * I * \52.33 ^(2)`

K1 = 1369.2 I

Final kinetic energy

`K_(2)=0.5 * I * \omega_(0)^(2)`

K2 = 0

Change in Kinetic energy = 1369.2 I

`I = 0.5 mr^(2)=0.5 * m * 1.2 * 1.2=0.72 m`

So, Work done

2.3 x 1000 = 1369.2 x 0.72 m

2300 = 985.82 m

m = 2.3 kg

Option (B)