Question

# 3. A flywheel comprises a uniform circular disk with a mass of 112.0 kg and a...

3.
A flywheel comprises a uniform circular disk with a mass of 112.0 kg and a radius of 1.3 m. It rotates with an angular velocity of 1213 rev/min. A constant tangential force is applied at a radial distance of 0.8 m. What is the initial kinetic energy of the wheel?

4.
If the wheel is brought to rest in 111.0 s, what is the tangential force?

5.
How many revolutions does the flywheel make while it is stopping in time 111.0 s?

3.

kinetic energy:

K = (1/2)I ω²

= (1/2)(0.5 m r²) (2πf)²

=(1/2)(0.5* 112* 1.3²) (2π * 1213/60)²

= 7.6275 * 10^5 J

4.

Angular acceleration: α = -F d/(0.5*m r²)

the force is calculated as follows:

ω = ωo + α t

0 = 2πf -F t d/(0.5 m r²)

0 = 2π * 1213/60 -F (111)(0.8)/(0.5 * 112* 1.3²)

F = 135.3 N

5.

rotational kinematic equation: ω² = ωo² + 2α θ

the angular displacement is,

0 = (2πf)² + 2α θ

0 = (2πf)² + 2(-F d/(0.5 m r²)) θ

0 = (2π * 1213/60)² +2(-135.3 * 0.8/(0.5 * 112* 1.3²)) θ

or

θ = 1122.11 rev

note: 1 rev = 2π rad