Write the law of conservation of angular momentum! A wheel is rotating at angular velocity! Its rotation axis is vertical! On the axis of this wheel, another wheel is slowly mounted in the stoppage! And these two wheels rotate simultaneously at the same angular velocity! If the radius of the second wheel is equal to the radius of the first wheel, but its mass is half the mass of the first wheel, then calculate the combined velocity of both wheels?
Answers
Explanation:
Let the moment of inertia of the wheel abut the axis be I. Initially the first wheel is rotating at the angulr speed `omega` about the axle and the second wheel is at rest. Take both the wheels together as the system. The total angular momentum of the system before the coupling is `Iomega+0=Iomega`. When the second wheel is droipped into the axle, the two wheels slip on each other and exert forces of friction. The forces of friction have torques about teh axis of rotation but these ar torques of interN/Al forces. No exterN/Al torque is aplied on the two wheel system and hence the angular momentum of the system remains unchanged. If the common angular speed is `omega` the total angular momentum of the two wheel system is `2Iomega` after the coupling. thus, <br> `Iomega=2Iomega` <br> `or omega'=omega/2`