What is the torque exerted by the flywheel on the machine?

[traviata]

Homework Statement

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 2.0 m diameter and a mass of 260 kg . Its maximum angular velocity is 1400 rpm .

1. The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.5 s . What is the average power delivered to the machine?
2. How much torque does the flywheel exert on the machine?

Homework Equations

P=τ⋅ω

The Attempt at a Solution

From working out earlier parts of the problem, I already have:

ω=1400rpm*(min/60s)*(2π rad/rev) = 146.61 rad/s
P = ΔE/Δt = ½K_max/Δt = 1/8*m(ωr)²/Δt = 1/8*(260kg)*(146.61rad/s*1.0m)² = 2.794*10⁵ W

Mastering Physics marks this as correct. However, when I solve for torque in terms of power and angular velocity

τ = P/ω = 2.794*10⁵ W / 146.61 rad/s = 1905.9 N*m

Master Physics marks 1900 N*m (it requires 2 significant figures), as incorrect. Any suggestions?

 

[haruspex]

τ = P/ω

Will ω be constant?

 

[traviata]

ω is not constant, as the kinetic energy of the flywheel changes.

 

[haruspex]

ω is not constant, as the kinetic energy of the flywheel changes.

So what value can you use in P/ω?

 

[traviata]

Are you saying I can't use ω because it's not constant. Is there another equation I have to use?

 

[haruspex]

Are you saying I can't use ω because it's not constant. Is there another equation I have to use?

Rotational systems such as this are highly analogous to linear systems.
If you had a moving mass that loses half its (known) KE in a known time under constant force, could you find that force?