Assignment 1:
1. Three mass points $m_1$, $m_2$ and $m_3$ are located at the vertices of an equilateral triangle of length $a$. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through $m_1$?
2. Four particles of masses $4\;kg$, $2\;kg$, $3\;kg$ and $5\;kg$ are respectively located at the four corners $A$, $B$, $C$ and $D$ of a square of side $1\;m$. Calculate the moment of inertia of the system about:
(i) an axis passing through the point of intersection of the diagonals and perpendicular to the plane of the square,
(ii) the side $AB$,
(iii) the diagonal $BD$.
Assignment 2:
3. A wheel is rotating at a rate of 1000 rpm & its kinetic energy is $10^6$ J. Determine the moment of inertia of the wheel about its axis of rotation.
4. Find (i) the radius of gyration & (ii) the MI of the rod of mass $100\; gm$ and length $100 \; cm$ about an axis passing through its center & perpendicular to its length.
5. Calculate the angular momentum of the earth rotating about its own axis. Mass of the earth is $5.98 * 10^{24}\; kg$, Mean radius of earth is $6.37 * 10^6\; m$, MI of the earth is $\frac{2}{5}MR^2$.
6. The moment of inertia od the wheel is $1000\; kgm^2.$ At a given instant, its angular velocity is $10 \; rad/s$. After the wheel rotates through an angle $100$ radians, the wheels angular velocity is $100\; rad/s$. Calculate (i) the torque applied on the wheel. (ii) the increase in rotational KE.
7. A ballet dancer stretches her arms to reduce her motion. Explain.
8. If earth contracts to half its radius, what would be the length of the day?
9. Explain why spokes are fitted in the cycle wheel.
10. A fan with blades takes longer time to come to rest than without the blades. Why?
11. If the earth is struck by meteorites, the earth will slow down slightly. Why?
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