- Introduction
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- Angular velocity and angular acceleration
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- Rotation with constant angular acceleration
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- Kinetic energy of Rotation
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- Calculation of moment of inertia
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- Theorems of Moment of Inertia
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- Torque
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- work and power in rotational motion
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- Torque and angular acceleration
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- Angular momentum and torque as vector product
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- Angular momentum and torque of the system of particles
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- Angular momentum of the system of particles with respect to the center of mass of the system
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- Radius of gyration
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- Kinetic Energy of rolling bodies (rotation and translation combined)
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- Solved examples

- Consider a system of particles made up of number of particles, moving independently to each other. Let L
_{1}, L_{2},L_{3},.............etc. be the angular momentum of different particles of the system w.r.t., to a given point.

- The angulat momentum of the particle system w.r.t. that given point is equal to the vector sum of angular momentum of all the particles of the system.

- If
**L**is the angular momentum of the system of particles or the body as a whole then,

- Torque acting on the system of particles from equation above angular momentem of the system of particles is given as

- When particles of the system are in motion then their motion is due to external and interaction due to internal forces so force acting on any particle of the system is given by

Here F_{iext}is the external force acting on the ith particle and ∑F_{ij}is the sum of the force acting on the particle due to internal interaction of different particles.Putting the value of**F**in the equation we get_{i}

- RHS of the equation 2 shows that summantion of the moment of interacting force (internal) .Here internal interaction forces balance each other so torque due to internal forces adds to zero hence

- Above equation proves that total torque acting on a system of particles is equal to the vector sum of the torque acting on the different particles due to external force on the particle and its value is also equal to the rate of change of angular momentum

Class 11 Maths Class 11 Physics Class 11 Chemistry