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

Answer:

t = 1767.43 s

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

 $I = \dfrac{1}{2}MR^2$

 $I = \dfrac{1}{2}\times 250 \times 0.75^2$

        I = 70.3125 Kg.m²

we know,

    τ = I α

    $\alpha = \dfrac{\tau}{I}$

    $\alpha = \dfrac{50}{70.3125}$

           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