Here are the most important short questions and answers from the topic Rotational Dynamics from Grade XII Physics.
1. Why is the moment of inertia also called rotational inertia ?
The moment of inertia gives the measure of inertia in rotational motion. So it is also called rotational inertia.
2. Why is it more difficult to revolve a stone tied to a large string than a stone tied to a short string?
The length of the string increases the distance of rotating mass from the axis of rotation and hence the moment of inertia of the system is increased. Now, τ = Iα thus a system with a large moment of inertia requires large torque for its rotation.
3. Why there are two propellers in the helicopter?
If there were only one propeller in the helicopter then due to the conservation of angular momentum, the helicopter itself would have turned in the opposite direction.
4. The speed of a whirlwind in a tornado is alarmingly high, why?
In a whirlwind, the air from nearby regions gets concentrated in a small space thereby decreasing the value of the moment of inertia considerably. Since, Iω = constant, due to the decrease in moment of inertia, the angular speed becomes quite high.
5. If the earth is struck by meteorites, the earth will slow down slightly. Why?
If the earth is struck by meteorites, some mass is added to it so its moment of inertia increases. According to the law of conservation of angular momentum Iω = constant, its angular speed ( ω ) decreases as I increase, so the earth will slow down.
6. Why spokes are fitted in cycle wheels?
The cycle wheel is so constructed so as to increase its moment of inertia with the minimum possible mass. The greater the moment of inertia, the greater the opposition to any charge in uniform rotational motion. As result, the cycle runs smoother and steadier. If the cycle wheel had no spokes, the cycle would be driven in jerks and hence unsafe.
7. Will two spheres of equal masses, one solid and the other hollow have equal moments of inertia? Give reason.
The hollow sphere will have a greater moment of inertia because its entire mass is concentrated at the boundary of the sphere i.e, at maximum distance from the axis of rotation.
8. Explain if the ice on the polar caps of Earth melts, how will it affect the duration of the day?
If the ice on the polar caps of the Earth melts, the water so formed will spread on the surface of the earth. This increase the moment of inertia (I) of the earth about its own axis (due to a change in the distribution of mass of the particles of water going away from the axis of rotation). To conserve angular momentum ( Iω ), ω (angular velocity of Earth about its own axis) will decrease. As T = 2π/ω, hence due to a decrease in the value of ω, T i.e. the duration of the day will increase.
9. The angular velocity of the earth around the sun increases, when it comes closer to the sun. Why?
When the Earth comes closer to the sun, its moment of inertia about the axis through the sun decreases. To conserve angular momentum( L = Iω ), the angular velocity of the Earth increases.
10. A fan with blades takes a longer time to come to the rest than without the blades, why?
The mass of the fan with blades is more than the fan without the blades so the moment of inertia of the fan with blades is more. According to the law of conservation of angular momentum, Iω = constant, its angular speed is less but ω = 2π/T, so time will take more. In another word, we can say that a fan with blades takes a longer time to come to rest than one without blades.
11. Can a single force applied to a body change both its translational and rotational motion? Explain.
A single force can change only translational motion, not rotational motion. This is because only torque can produce rotational motion for which a pair of forces having the same magnitude but opposite in direction in different lines of action is required.
12. A cat is able to land on a foot after a fall. Why?
When a cat falls to the ground from a height, it stretches its body along with the tail so that its moment of inertia becomes high. Since Iω = constant, the value of angular speed ω decreases, and therefore the cat is able to land on the ground gently.
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