SOME IMPORTANT QUESTION AND 
ANSWERS OF PHYSICS
Rotational Dynamics:
Rotational dynamics is a branch of mechanics which deals with the study of the rotational motion of a rigid body rotating about an axis. Rigid Body A rigid body is an assembly of a large number of particles. In a rigid body, the inter-particle distances remain the same when it is acted upon by an external force or torque. For all practical purposes, all solids can be regarded as rigid bodies because the yielding in solids is very small. Moment of Inertia of a Rigid Body The moment of inertia of a rigid body about an axis is defined as the sum of the product of masses of the particles constituting the body and the square of their respective perpendicular distances from that axis of rotation .
Radius of Gyration:
The radius of gyration of a rigid body about an axis is defined as the distance from the axis of rotation where the total mass of the body is supposed to be concentrated so that the moment of inertia of the body about that axis remains the same.
Angular Momentum :
The angular momentum of a rigid body about an axis is defined as the moment of the linear momentum of the body about that axis and is denoted by L. It is measured by the product of the linear momentum p and the perpendicular distance r of its line of action from the axis of rotation.
Conceptual Q1: A fan with blades takes longer time to come to rest than without the blades, why? It is obvious that the rotational inertia of a fan with blades is greater than that of a fan without blades. According to Newton's first law of motion, rotational inertia always opposes the changes in the states of rotation of a body or rest. Therefore the greater a rigid body such as the fan with blades has its rotational inertia, the more it is difficult to change its rotational motion into rest. For this reason, the fan with blades takes longer time to come to rest than the one without blades.
Conceptual Q2: You are provided with a hardboiled egg and a raw egg. How will you distinguish between the two? We can distinguish between the two by spinning them on a table top. The hardboiled egg will spin faster and longer for it is nearly a rigid spherical body. On the other hand, while the raw egg spins, the thick fluid matter in it tries to move away from the axis of rotation, increasing its moment of inertia. This results in lowering the angular velocity and hence the raw egg will spin slower and comes to rest earlier than the hard boiled one.
Conceptual Q3: When an acrobat walks on a tightrope, she extends her arms straight out from her sides. She does this to make it easier for her to catch herself if she should tip to one side or the other. Explain how this works.
An acrobat walking on a tightrope extends her arms, straight out from her sides when she starts tipping to one side or the other. On one hand, she will increase her moment of inertia about the rope by extending her arms. On the other hand, she will decrease her angular acceleration to the least as far as possible. Therefore the net torque applied on her will be zero. This is why she needs to extend her arms while she walks on the rope.
Moment of Inertia as the Rotational Inertia
In rotational dynamics, the value of inertia not only depends upon the mass of a body but also depends upon the distribution of its mass. Moment of inertia of the body is equal to the sum of the product of the masses of particles constituting the body and the square of their respective distances from an axis of rotation. Actually the moment of inertia of the body resists any change in the states of rotational motion or rest. So the moment of inertia is also called rotational inertia.
The Principle of Conservation of Angular Momentum
It states that the angular momentum of a rigid body about an axis remains constant if there is no external torque acting about that axis. Suppose a rigid body of moment of inertia I is rotating with a constant angular velocity at any instant. Thus the angular momentum of the body is L = I w
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Conceptual Q4: Explain why spokes are fitted in the cycle wheel. When spokes are fitted in the cycle wheel, the mass is mainly distributed on the rim. This increases the moment of inertia of the wheel with minimum possible mass. This has two advantages: first, the cycle becomes light and portable and second, high moment of inertia of the wheel ensures uniform speed and safety
Conceptual Q5: If the earth is struck by meteorites, the earth will slow down slightly. Why? Conceptual Q6: The construction of a high and large dam for generating hydropower is opposed by the environmentalists. Can you support their conviction in terms of physical laws?