Question

Two thin rectangular sheets (0.16 m x 0.44 m) are identical. In the first sheet the axis of rotation lies along the 0.16-m side, and in the second it lies along the 0.44-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

Answer:

$t'=1.124s$

Explanation:

$I_b*a_b=I_a*a_a$

$a_a=\frac{w_f}{t'}$

$a_b=\frac{w_f}{t}$

$I_b*\frac{w_f}{t}=I_a*\frac{w_f}{t'}$

$I_b*\frac{1}{t}=I_a*\frac{1}{t'}$

$I=\frac{1}{3}*M*r^2$

$I_a=\frac{1}{3}*M*r_a^2$

$I_b=\frac{1}{3}*M*r_b^2$

$\frac{1}{3}*M*r_b^2*\frac{1}{t}=\frac{1}{3}*M*r_a^2*\frac{1}{t'}$

$t'=(\frac{r_a}{r_b})^2 *t$

$t'=(\frac{0.16m}{0.44m})^2*t$

$t'=\frac{16}{121}*8.5s$

$t'=1.124s$