Question

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 Kg. Its maximum angular velocity is 12000 rpm.A motor spins up the flywheel with a constant torque of 50 Nm. How long does it take the flywheel to reach top speed?

Answer 1

t = 1767.43 s

Step-by-step explanation:

given,

diameter of fly wheel = 1.5 m

mass = 250 Kg

angular speed = 12000 rpm

= 12000 x 2π/60

= 1256.64 rad/s

torque = 50 Nm

moment of inertia of disk

`I = (1)/(2)MR^2`

`I = (1)/(2)* 250 * 0.75^2`

I = 70.3125 Kg.m²

we know,

τ = I α

`\alpha = (\tau)/(I)`

`\alpha = (50)/(70.3125)`

α = 0.711 rad/s²

using equation of rotational motion

ω = ω₀ + α t

1256.64 = 0 + 0.711 x t

t = 1767.43 s