A flywheel is auniform disc of mass 72kg and radius 50cm. Calculate a. the moment of inertia and

Question

b. it's kinetic energy when it is rotating at 70r.p.m

Answer 1

To calculate the moment of inertia of the flywheel, we use the formula for the moment of inertia of a disc:

I = (1/2) * m * r^2

where I is the moment of inertia, m is the mass of the disc, and r is the radius of the disc.

Given that the mass of the flywheel is 72 kg and the radius is 50 cm (or 0.5 m), we have:

I = (1/2) * (72 kg) * (0.5 m)^2
I = 9 kg * m^2

So, the moment of inertia of the flywheel is 9 kg * m^2.

To calculate the kinetic energy of the flywheel, we use the formula for rotational kinetic energy:

KE = (1/2) * I * ω^2

where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity, given in radians per second.

First, we need to convert the rotational speed from revolutions per minute (r.p.m.) to radians per second (rad/s):

ω = 2π * n / 60

where n is the number of revolutions per minute.

Given that the flywheel is rotating at 70 r.p.m., we have:

ω = 2π * 70 / 60
ω ≈ 7.33 rad/s

Now we can substitute the values into the formula:

KE = (1/2) * (9 kg * m^2) * (7.33 rad/s)^2
KE ≈ 228.24 J

So, the kinetic energy of the flywheel when it is rotating at 70 r.p.m. is approximately 228.24 J.