Question

A square plate has mass 0.600 kg and sides of length 0.150 m. It is free to rotate without friction around an axis through its center and perpendicular to the plane of the plate. How much work must you do on the plate to change its angular speed from 0 to 40.0 rad/s?

Answer 1

Answer:

 W = 1.8 J

Explanation:

given,

mass of square plate = 0.6 Kg

length of side of square plate = 0.15 m

speed is change from   0 to 40.0 rad/s

work done = ?

moment of inertia through the plane perpendicular to plane

$I = \dfrac{Mr^2}{6}$

r will be equal to 0.15 m

$I = \dfrac{0.6 \times 0.15^2}{6}$

$I =0.00225\ kgm^2$

work done is equal to change in kinetic energy

 $W = \dfrac{1}{2}I(\omega_f^2-\omega_i^2)$

 $W = \dfrac{1}{2}\times 0.00225(40^2-0^2)$

   W = 1.8 J

work done when speed changes from 0 to 40 rad/s is equal to  W = 1.8 J