State an expression for the moment of inertia of a solid sphere about its diameter. Write the expression for the corresponding radius of gyration.
Q 85
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Two discs of moments of inertia $\mathrm{I}_1$ and $\mathrm{I}_2$ about their transverse symmetry axes, respectively rotating with angular velocities to $\omega_1$ and $\omega_2$, are brought into contact with their rotation axes coincident. Find the angular velocity of the composite disc.
A stone of mass $100 \mathrm{~g}$ attached to a string of length $50 \mathrm{~cm}$ is whirled in a vertical circle by giving it a velocity of $7 \mathrm{~m} / \mathrm{s}$ at the lowest point. Find the velocity at the highest point.
A coin is placed on a stationary disc at a distance of $1 \mathrm{~m}$ from the disc's centre. At time $t=0$ $\mathrm{s}$, the disc begins to rotate with a constant angular acceleration of $2 \mathrm{rad} / \mathrm{s}^2$ around a fixed vertical axis through its centre and perpendicular to its plane. Find the magnitude of the linear acceleration of the coin at $t=1.5 \mathrm{~s}$. Assume the coin does not slip.