While spinning down from 500 rpm to rest, a flywheel does 3.9 kj of work. this flywheel is in the shape of a solid uniform disk of radius 1.2 m. what is the mass of this flywheel?

The answer is 4.0 kg since the flywheel comes to rest the kinetic energy of the wheel in motion is spent doing the work. Using the formula KE = (1/2) I w².

Given the following:

I =  the moment of inertia about the axis passing through the center of the wheel; w = angular velocity ; for the solid disk as I = mr² / 2 so KE = (1/4) mr²w². Now initially, the wheel is spinning at 500 rpm so w = 500 * (2*pi / 60) rad / sec = 52.36 rad / sec.

The radius = 1.2 m and KE = 3900 J

3900 J = (1/4) m (1.2)² (52.36)²

m = 3900 J / (0.25) (1.2)² (52.36)²

m = 3.95151 ≈ 4.00 kg

The mass of the flywheel in the shape of a solid uniform disk of radius 1.2 m is 4 Kg.

Given :

N = 500 rpm

Work = 3.9 KJ = 3900 J

Radius = 1.2 m

Solution :

We know that the angular velocity is given by:

We know that the Moment of Inertia for solid disk is given by:

--- (1)

Now kinetic energy in terms of angular velocity is given by:

---- (2)

From equation (1) and (2) we get,

  ---- (3)

Now put the values of KE, r and in equation (3) we get:

m = 3.9515 Kg

m 4 Kg

The mass of the flywheel in the shape of a solid uniform disk of radius 1.2 m is 4 Kg.

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