A flywheel is auniform disc of mass 72kg and radius 50cm. Calculate a. the moment of inertia and
b. it's kinetic energy when it is rotating at 70r.p.m
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.