Question

a wheel of moment of inertia 30kg m square is rotating at 10 rotation per minute .the work done in increasing its speed to 5 times its intial value will be ??????????????????????/

Answer 1

Work is difference between the first and the second value of energy.

$$A = \Delta E$$ $$E - \text{energy}$$ $$A - \text{work}$$ $$E = \frac{I \cdot w^2}{2}, \text{where}$$ $$I - \text{Moment of inertia};$$ $$w - \text{Angular velocity}.$$ $$I = 30 \frac{kg}{m^2}, \quad w = 10 \text{ rotation per minute} = 1.05 \frac{rad}{s}$$ $$E_1 = \frac{30 \cdot 1.05}{2} = 15.75 \, \text{J}$$

If we increase velocity, we will have:

$$w = 5.25 \frac{rad}{s}$$ $$E_2 = \frac{30 \cdot 5.25}{2} = 78.75 \, \text{J}$$ $$A = 78.75 - 15.75 = 63 \, \text{J} - \text{the work done in increasing wheels speed}$$