Question

In: Physics

A flywheel comprises a uniform circular disk with a mass of 97.0 kg and a radius...

A flywheel comprises a uniform circular disk with a mass of 97.0 kg and a radius of 1.1 m. It rotates with an angular velocity of 1420 rev/min. A constant tangential force is applied at a radial distance of 0.5 m. What is the initial kinetic energy of the wheel?

(b) If the wheel is brought to rest in 133.0 s, what is the tangential force?

Expert Solution

Mass of the flywheel = M = 97 kg

Radius of the flywheel = R = 1.1 m

Moment of inertia of the flywheel = I

I = 58.685 kg.m²

Initial angular velocity of the flywheel = ₁ = 1420 rev/min = 1420 x (2/60) rad/s = 148.7 rad/s

Initial kinetic energy of the flywheel = E₁

E₁ = 6.49 x 10⁵ J

Final angular velocity of the flywheel = ₂ = 0 rad/s (Brought to rest)

Time period in which the flywheel is brought to rest = T = 133 sec

Angular acceleration of the flywheel =

= -1.118 rad/s²

Negative as it is deceleration.

Tangential force acting on the flywheel = F

Radial distance at which the tangential force acts = r = 0.5 m

Torque due to the tangential force on the flywheel =

= -Fr (Negative as it is opposing the motion of the flywheel)

F = 131 N

a) Initial kinetic energy of the flywheel = 6.49 x 10⁵ J

b) Tangential force on the flywheel = 131 N

genius_generous answered 1 year ago

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