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A flywheel has a 135-kg solid cylindrical rotor with radius 30 cm and spins at 31,000 rpm. How much energy does it store?
Anonymous
Jan 29
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#flywheel
#energy
#physics
A flywheel has a 135-kg solid cylindrical rotor with radius 30 cm and spins at 31,000 rpm. How much energy does it store?
A flywheel has a 135-kg solid cylindrical rotor with radius 30 cm and spins at 31,000 rpm. How much energy does it store?
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Jan 29
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To calculate the energy stored in the flywheel, we need to use the formula for rotational kinetic energy:
E = (1/2) I ω^2
Where:
E is the energy stored in the flywheel
I is the moment of inertia of the flywheel
ω is the angular velocity of the flywheel
The moment of inertia of a solid cylindrical rotor can be calculated using the formula:
I = (1/2) m r^2
Where:
m is the mass of the rotor
r is the radius of the rotor
Given:
m = 135 kg
r = 30 cm = 0.3 m
ω = 31,000 rpm = (31,000/60) rad/s = 516.67 rad/s
First, let's calculate the moment of inertia:
I = (1/2) m r^2
I = (1/2) * 135 kg * (0.3 m)^2
I = 6.075 kg·m^2
Now, let's calculate the energy stored in the flywheel:
E = (1/2) I ω^2
E = (1/2) * 6.075 kg·m^2 * (516.67 rad/s)^2
E = 0.5 * 6.075 kg·m^2 * 267,223.89 rad^2/s^2
E = 805,180.34 Joules
Therefore, the flywheel stores approximately 805,180.34 Joules of energy.
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