Moment of inertia and rotational kinetic energy

[pb23me]

Homework Statement

A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutions per 8.00s? Assume it is a solid cylinder.

Homework Equations

$\Delta$KE=Wnet=1/2(Iw²)=14211.7J
$\tau$=($\Delta$w/$\Delta$t)

The Attempt at a Solution

I tryed to get the answer by finding net torque first, but i didnt think i could find the net torque because i don't have the time that the merry go round goes from zero to w=.785rad/s.Then i just used the change in kinetic energy equation to get 14211.7J could i have found this answer the other way?

 

[collinsmark]

$\Delta$KE=Wnet=1/2(Iw²)=14211.7J
$\tau$=($\Delta$w/$\color{red}{\Delta}$t)

You used the wrong variable! :tongue: It should be Δθ, not Δt

$\tau$ = (ΔW)/(Δθ)​

The Attempt at a Solution

I tryed to get the answer by finding net torque first, but i didnt think i could find the net torque because i don't have the time that the merry go round goes from zero to w=.785rad/s.Then i just used the change in kinetic energy equation to get 14211.7J could i have found this answer the other way?

Yes. You could use kinematics if you wanted to. (But the work-energy theorem, which you ended up using in the end, is much easier.)

If you wanted to use kinematics, use the following equations:

• W = $\tau$·θ (definition of work, assuming uniform torque)
• $\tau$ = Iα (Newton's second law in angular terms)
• ω_f² - ω_i² = 2αθ (one of your angular kinematics equations).

Combine the equations and solve for W. (Hint: if you keep everything in terms of variables, and solve for W before substituting in specific numbers, you'll get a pleasing result! )

 

[pb23me]

thank you