A Flywheel with a mass of 320 Kg and radius of gyration of 26 cm accelerates from rest to 750 rpm in
10 seconds.
Calculate: the work done
To calculate the work done on the flywheel, we first need to find the moment of inertia of the flywheel using the formula:
I = m * k^2
Where:
I = moment of inertia
m = mass of the flywheel (320 kg)
k = radius of gyration (26 cm = 0.26 m)
I = 320 kg * (0.26 m)^2
I = 32.64 kg.m^2
Next, we need to calculate the final angular velocity of the flywheel in radians per second, which is given as 750 rpm. We convert this to radians per second:
Angular velocity (ω) = 750 rpm * (2π radians / 1 revolution) * (1 minute / 60 seconds)
ω = 78.54 radians/second
Now, we can calculate the kinetic energy of the flywheel using the formula:
Kinetic energy = 1/2 * I * ω^2
KE = 0.5 * 32.64 kg.m^2 * (78.54 radians/second)^2
KE = 101,750.45 Joules
The work done on the flywheel can be calculated as the change in kinetic energy, which is given by:
Work done = KE final - KE initial
Work done = 101,750.45 J - 0 J
Work done = 101,750.45 Joules
Therefore, the work done on the flywheel is 101,750.45 Joules.