A horizontal circular platform of radius 0.5m and mass 0.45kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05kg are attached to the platform at a distance 0.25m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the ball horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the ball have horizontal speed of 9ms−1 with respect to the ground. The rotational speed of the platform in rads−1 after the balls leave the platform is :
Using the principle of Angular momentum conservation,
L1=L2
or
I1ω1=(mvr)2
or
(0.4×0.5×0.52)ω1=2×0.05×9×0.52
Thus ω1=4
A disc of mass m and radius R is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass m/2 each, are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity ω0 and released.
The speed of each ball relative to the ground just after they leave the disc is
A horizontal square platform of mass m and side a is free to rotate about a vertical axis passing through its centre O. The platform is stationary and a person of the same mass (m) as the platform is standing on it at point A. The person now starts walking along the edge from A to B ( see figure). The speed v of the person with respect to the platform is constant. Taking v=5 m/s and a = 1 m,
A kid of mass 50 kg stands at the edge of a platform of radius 1 m which can be freely rotated about its axis. The moment of inertia of the platform is 0.02 kg-m2. The system is at rest. The kid throws a ball of mass 2 kg horizontally to his friend (friend standing on the ground) in a direction tangential to the rim with a speed 10 m/s as seen by his friend. The angular velocity with which the platform will start rotating in rad/s is
