Two thin rectangular sheets (0.17 m 0.41 m) are identical. In the first sheet the axis of rotation lies along

Question

Two thin rectangular sheets (0.17 m 0.41 m) are identical. In the first sheet the axis of rotation lies along the 0.17 m side, and in the second it lies along the 0.41 m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 8.5 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?

Answer 1

I will use T=I*alpha
or for simplicity
T=I*a
which can also be expressed as
T/I=a

Both sheets have the same mass, m
for the first,
I1=.25*m*.41^2

for the second
I2=.25*m*.17^2
Both were computed as m*(L/2)^2

I will assume constant angular acceleration (no friction), so
w(t)=a*t
since the w for both are equal and the first reaches w in 8.5 seconds, then
w=a1*8.5
from above
w=8.5*T/I1

for the second
w=t*T/I2
since the w is the same
t*T/I2=8.5*T/I1
solving for t
t=8.5*I2/I1
from above
t=8.5*.25*m*.17^2/(.25*m*.41^2)
simplify
t=8.5*(.17/.41)^2

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