conservation of angular momentum solved numericals

 

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A spherical water balloon is revolving at 60 rpm. In the course of time, 48.8 % of its water leaks out. With what frequency will the remaining balloon revolve now? 

Q5. A ballet dancer spins about a vertical axis at 90 rpm with arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes to 75%. Calculate the new speed of rotation.
 

Q9. Two wheels of moment of inertia 4 kgm2 rotate side by side at the rate of 120 rev/min and 240 rev/min respectively in the opposite directions. Iff now both the wheels are coupled by means of weightless shaft so that both the wheels now rotate with a common angular speed, Find the new speed of rotation
 

Q10. A uniform circular disc with its plane horizontal is rotating about a vertical axis passing through its centre at a speed of 180 r.p.m. A small piece of wax of mass. 1.9 g falls vertically on the disc and sticks to it at a distance of 25 cm from the axis. If the speed of rotation is now reduced by 60 r.p.m., calculate moment of inertia of the disc.
 

Q12. A homogeneous rod XY of length L and mass `M' is pivoted at the centre 'C' such that it can rotate freely in vertical plane. Initially the rod is in the horizontal position. A blob of wax of same mass 'M' as that of the rod falls vertically with the speed 'V' and sticks to the rod midway between points C and Y. If the rod rotates with angular speed 'w' what will be angular speed in terms of V and L ?

Q20. A big dumb-bell is prepared by using a uniform rod of mass 60g and length 20cm. Two identical solid spheres of mass 50g and radius 10cm each are at the two ends of the rod. Calculate the moment of about an axis passing through its center and perpendicular to the length.


Q21. A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the centre. Calculate x if the wheel now rotates at 80 rpm.