equal, then (a) Kinetic energy of A= Kinetic energy of B (b) Kinetic energy of A> Kinetic energy

Equal, then (a) Kinetic energy of A= Kinetic energy of B (b)...

Key Concepts

Dependence on Mass in Equal Momentum Conditions

When two bodies have the same momentum, their kinetic energies will differ based on their masses. Specifically, the body with the smaller mass will have a greater kinetic energy because the kinetic energy increases as the mass decreases for a given momentum.

Relationship between Kinetic Energy and Momentum

There is a fundamental relationship between kinetic energy and momentum described by the formula K = p²/(2m), where p represents linear momentum and m is the object's mass. This shows that for a given momentum, kinetic energy is inversely proportional to the mass.

Kinetic Energy

Kinetic energy is a scalar quantity that represents the energy an object possesses due to its motion. It is given by the expression (1/2) times mass times the square of velocity, and it quantifies the work required to accelerate an object from rest to its current velocity.

Linear Momentum

Linear momentum is a vector quantity defined as the product of an object's mass and its velocity. It measures the quantity of motion an object has and plays a central role in analyzing collision and conservation scenarios in mechanics.

Transcript

00:01 So here the question it is asked that the moment of inertia of two rotating bodies a and b are ia and i b and i b and it is given that ia is greater than i b so i'm just writing that value here given that ia is greater than i b and the next point it is given is if their angular momentum are equal then what is the correct statement from the given options.

00:30 Now, what is the equation for angular momentum? so, angular momentum is a momentum is equal to i into omega here.

00:46 I is the, i is the moment of inertia and omega is the rotational velocity.

00:53 So just like in translational motion we have, the momentum equation for momentum is mass into velocity so similarly similar or mass is equivalent to angular moment of inertia in rotational motion and this velocity is equivalent to angular velocity so i into omega is the equation to find angular momentum now we have to find which statement from that is correct and all the statements are related to kinetic energy only and we know that kinetic energy in rotation is even to half i omega square which is very similar to half mv square in translational motion so we would have to find this kinetic energy of both the objects a and b now it is given that amplar momentum is equal then we can write that i a into omega a is equal to i b into omega b from this we can write that omega a divided by omega b because i'm just taking this omega b to this side and this i a to this side then we can write omega a divided by omega b which will be equal to i b divided by ia so this is the one thing that we can conclude from the given statement now now we have the equation to find the acceleration so if sorry the kinetic energy so if we write that kinetic energy of a that will be is equal to half ia into omega a square and similarly kinetic energy of b will be equal to half i b into omega b square and if i am taking kinetic energy of a divided by kinetic energy of b then this will be equal to half ia omega a square divided by half i b omega b square here half and half will be cancelled each other so that i can write it as ia divided by ib.

03:05 So this will be the first part into omega a divided by omega b.

03:11 And i'm giving this square to both...

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