Math Is Fun Forum

woca

Member

Registered: 2006-01-14

Posts: 4

Moment of Inertia, Potential energy, Velocity Problems (2)

Problem 1

Example A flywheel consists of a uniform steel disc of mass 20 kg and diameter
0.4m. It is lifted vertically 200m, and placed on an incline. The flywheel is then
released and rolls down the incline without slipping.

Find:
(a) the moment of inertia of the flywheel;
(b) the potential energy;
(c) the maximum linear velocity of the disc as it reaches the bottom of the incline;
(d) the maximum angular velocity.

Problem 2

A flywheel, of mass 500 kg, takes the form of a uniform disc of
diameter 1.5 m. The flywheel is fastened to a horizontal shaft lying in
bearings and is coupled to an electric motor.

Find:
(a) the moment of inertia of the flywheel assuming the contribution of the shaft is
negligible;
(b) the torque at the motor to give the flywheel/shaft system an acceleration of 6
rad/s2;
(c) the power transmitted by the motor when a speed of 500 rev/min has been
attained;
(d) the height a mass of 2000 kg will be raised before the flywheel comes to rest. The
mass is fastened to a rope which is wrapped around a drum, which, in turn, is keyed to
the flywheel shaft. When the flywheel reaches a speed of 650 rev /min the motor is
disconnected and the flywheel/drum system is allowed to rotate freely.

Post workings out and answers here. I will also give them ago:)

ryos

Member

Registered: 2005-08-04

Posts: 394

Re: Moment of Inertia, Potential energy, Velocity Problems (2)

The potential energy in problem 1 is given by U = mgy. That's 20 kg * 9.8 m/sec² * 200 m = 39,200 J.

I looked up the moment of inertia for a disk; it's I = 1/2MR². So for this disk, I = 1/2 * 20kg * (0.2m)² = 0.4kg*m²

To find the angular acceleration α, you need the angle θ of the slope of the incline. Then, you can find the maximum angular velocity. Convert this velocity to kinetic energy, and subtract it from the total potential energy. The remaining potential energy was converted to linear velocity, which you can find by converting the remaining potential energy back into velocity.

Problem 2:

a)  I = 140.625 Kg * m².
b) I sort of neglected torque when I took physics. Someone else will need to answer, or you can ask your teacher.
c) I neglected Power too
d) What is the diameter of the drum?

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El que pega primero pega dos veces.