Rotational Motion About a Fixed Axis

[wchvball13]

Homework Statement

Two thin rectangular sheets (0.23 m 0.35 m) are identical. In the first sheet the axis of rotation lies along the 0.23 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 6.5 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?

Homework Equations

$$\tau=(mr^{2})\alpha$$
$$E\tau=I\alpha$$
$$I=(1/3)ML^{2}$$

The Attempt at a Solution

I don't know how to start if you don't have a mass...or the angular acceleration

 

[rl.bhat]

w = wo + alpha*t
Torque = I*alpha
Alpha = Torque/I
wo = 0 Torque is same, final angular velocity is same.
Therefore (Torque/I1)t1 = (Torque/I2)t2
I1 = (M* 0.35^2)/3 and I2 = ( M*0.23^2)/3

 

[Astronuc]

I don't know how to start if you don't have a mass...or the angular acceleration

The point is that the sheets are identical and the same torque is applied, but the moment of inertias will be different because of the different orientation, which means a different value for L in the expression for moment of inertia.

 

[wchvball13]

I understand both of your replies, but I still don't understand how I can solve it if I don't have M or alpha
I1 = (M* 0.35^2)/3 and I2 = ( M*0.23^2)/3

 

[rl.bhat]

w = wo + alpha*t...(1)
Torque = I*alpha...(2)
Alpha = Torque/I...(3)
wo = 0 Torque is same, final angular velocity is same.
Therefore (Torque/I1)t1 = (Torque/I2)t2...(4)
I1 = (M* 0.35^2)/3 and I2 = ( M*0.23^2)/3
From eq. 2 you can find alpha. Put this value in eq.1. Put wo = 0. and equate w for I1 and I2. In the final expression M gets canceled out.

 

[wchvball13]

apparently I suck at physics because I can't even understand how you can find Alpha from eq. 2. Once I figure out that I can find the rest but for right now all I have is I1=.0408 and I2=.0176...and that's if I ignore the masses since they're equal...

 

[rl.bhat]

From eq.4 you get t1/I1 = t2/I2, because torque is same. t1 = 6.5 s. Find t2.