Kinetic Energy of Rotation

[Audio] Hi everyone Today our topic is Kinetic energy of rotation.

[Audio] In linear motion the energy in a body due to its motion is called linear kinetic energy. Mathematically, kinetic energy equal to half m v square Similarly , the energy in a body due to its angular motion is called rotational kinetic energy and is given by kinetic energy rotation equal to half I omega square Where I equal moment of inertia of body Omega equal to angular velocity of body.

[Audio] Here are the some equations for linear and angular motion In linear motion S equal to v t In angular motion Theta equal to omega t In linear motion V f equal to v I plus a t In angular motion Omega f equal to omega I plus alpha t In linear motion Inertia equal to mass of body in angular motion Moment of inertia equal to m r square In linear motion Force equal to m a In angular motion Torque equal to I alpha In linear motion Momentum equal to m v In angular motion Momentum equal to I omega In linear motion Kinetic energy equal to half m v square in angular motion Kinetic energy equal to half I omega square.

[Audio] Here are the moment of inertia of different bodies For hoop For disc For cylinder For sphere And for rod Is shown in figure.

[Audio] Rolling of disc and hoop down the inclined plane A piece of thin walled cylinder or hollow sphere is called hoop or Thing ring Similarly a piece of solid cylinder is called disc as shown in figure A disc and hoop of mass m are allowed to move Along the inclined plane of slope They have two type of kinetic energy The linear kinetic energy And the rotational kinetic energy.

[Audio] to find velocity of disc When it rolls down According to law of conservation of energy Loss in potential energy equal to gain in kinetic energy Linear and rotational M g h equal to Half m v square plus half I omega square The inertia of disc is m r square Put values The velocity of disc is Under root 4 by 3 g h.

[Audio] Similarly for hoop Apply law of conservation of energy Loss in potential energy equal to Gain in kinetic energy M g h equal to Half m v square plus half I omega square Or V equal to under root g h Compare the velocities of disc and hoop we concluded that The velocity of disc is greater than hoop So if we inclined both bodies The disc will move faster than hoop and will reach bottom first.

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