Rectangular sheets, angular velocity time?

AI Thread Summary
Two identical rectangular sheets are analyzed for angular velocity under the same torque, with one rotating about a 0.26 m side and the other about a 0.35 m side. The first sheet reaches its final angular velocity in 7.3 seconds, prompting the question of how long it takes for the second sheet to achieve the same velocity. To solve this, the moment of inertia must be calculated for each axis of rotation, using the equation τ = Iα. The kinematic equation θ = 1/2(w0 + wf)*t can then be applied to find the time for the second sheet. Understanding the relationship between torque, moment of inertia, and angular acceleration is crucial for determining the solution.
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Homework Statement



Two thin rectangular sheets (0.26 m 0.35 m) are identical. In the first sheet the axis of rotation lies along the 0.26 m side, and in the second it lies along the 0.35 m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 7.3 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?
in seconds

Homework Equations





The Attempt at a Solution



how can this be figured out?

what is the theta?

i would use this equation theta = 1/2(w0 + wf)*t

and solve for wf.

not sure what theta is in the equation though.
 
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Use the equation

\tau\ = I\alpha}

From this you will get the moment of inertia. But beware this the moment of inertia about the 0.26m side. ..you will have to find it with respect to the o.35 side.Once done that again apply the above equation.

Then apply the kinematic equation and you will get the answer.
 
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