A horizontal wheel with buckets on its circumference revolves about a frictionless axis. Water falls into the buckets at a uniform rate of mass m per unit time. Treating the buckets as small compared

Question

A horizontal wheel with buckets on its circumference revolves about a frictionless axis. Water falls into the buckets at a uniform rate of mass m per unit time. Treating the buckets as small compared with the wheel, find the angle turned through by the wheel in time t. The moment of inertia of the wheel and buckets about the vertical axis is I and r is the radius of the circumference on which the buckets are placed. Initial angular velocity of the wheel system is $Ω$ .

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Answer:

C

Solution:

Incoming water increases the rotational inertia as I(t)=I+mtr².

Angular momentum is conserved: ω=IΩ/(I+mtr²).

Integrating angle gives θ=(IΩ/mr²) ln(1+mtr²/I).

TestHub · Accepted Answer

Incoming water increases the rotational inertia as I(t)=I+mtr². Angular momentum is conserved: ω=IΩ/(I+mtr²). Integrating angle gives θ=(IΩ/mr²) ln(1+mtr²/I).

Physics - Rotation Question with Solution | TestHub

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