What is the Angular Velocity?

[ymehuuh]

Homework Statement

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 270 N applied to its edge causes the wheel to have an angular acceleration of 0.984 rad/s2.

If the wheel starts from rest, what is its angular velocity after 4.30 s have elapsed, assuming the force is acting during that time?

Homework Equations

Moment of intertia is 90.457kg/m2
mass of wheel is 1661.29kg

The Attempt at a Solution

I was able to find moment of inertia and mass of wheel above...not sure about angular velocity. I can't find the right equation what uses I.

 

[ymehuuh]

nm...it was just w=at

 

[nlightner]

The angular velocity, ω, can be calculated using the equation ω = ω0 + αt, where ω0 is the initial angular velocity (in this case, 0 since the wheel starts from rest), α is the angular acceleration, and t is the time elapsed. Plugging in the given values, we get:

ω = 0 + (0.984 rad/s2)(4.30 s) = 4.2292 rad/s

Therefore, after 4.30 s, the wheel will have an angular velocity of 4.2292 rad/s.