A flywheel of mass 500kg and radius 1m make 500rev/min. Assuming the mass to be concentrated along the rim, calculate the energy of the flywheel
To calculate the energy of the flywheel, we can use the formula for the kinetic energy of a rotating object:
K.E. = (1/2) I ω^2
Where K.E. is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
First, we need to find the moment of inertia for the flywheel. The moment of inertia for a solid disk can be calculated using the formula:
I = (1/2) m r^2
Where m is the mass of the flywheel and r is the radius.
I = (1/2) (500 kg) (1 m)^2
I = 250 kg m^2
Now, we can find the angular velocity of the flywheel. The angular velocity is given in terms of revolutions per minute, so we need to convert it to radians per second:
ω = (500 rev/min) * (2π rad/rev) * (1 min/60 s)
ω = 52.36 rad/s
Now, we can calculate the kinetic energy of the flywheel:
K.E. = (1/2) I ω^2
K.E. = (1/2) (250 kg m^2) (52.36 rad/s)^2
K.E. = 346,132 J
Therefore, the energy of the flywheel is 346,132 Joules.