Posted by chelsea on Wednesday, May 30, 2012 at 8:31pm.
Two thin rectangular sheets (0.09 m 0.46 m) are identical. In the first sheet the axis of rotation lies along the 0.09m side, and in the second it lies along the 0.46m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 7.5 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?

physics  Elena, Thursday, May 31, 2012 at 8:11am
The moment of inertia of the rectangular plate about its side is
I =ma²/3 , where a is the length of another side (perpendicular to the axis of rotation), therefore,
I1 =m•(0.46)²/3,
I2 =m•(0.09)²/3,
Final angular velocity is
ω = ε1•t1, ε1 =ω /t1
ω = ε2•t2, • ε2 =ω /t2
The Newton’s 2 Law for rotation
M=I•ε,
M=I1• ε1 = I1• ω /t1= m•(0.46)² • ω /3•t1,
M=I2• ε2= I2• ω /t2 = m•(0.09)² • ω /3•t2,
m•(0.46)² • ω /3•t1 = m•(0.09)² • ω /3•t2,
(0.46)² /t1 =(0.09)² /t2,
t2 =t1• (0.09/0.46)² = 7.5•3.8•10^2= 0.28 s.
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