A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be _________rad   s - 1 .

Question

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is &#960; : 22 then, the value of its angular speed will be _________rad &#160; s - 1 .

Aicharya · Accepted Answer

The angular momentum is given by L = I C M &#969; = 2 M R 2 &#969; 5 The total kinetic energy is E = 1 2 ( M v 2 + 2 M R 2 &#969; 2 5 ) The ratio of angular momentum and kinetic energy is L E = I C M &#969; 1 2 M v 2 + 1 2 &#183; 2 5 M R 2 &#969; 2 = 2 5 M R 2 &#969; 7 10 M R 2 &#969; 2 &#8658; &#960; 22 = 4 7 &#183; 1 &#969; &#8658; &#969; = 4 &#160; rad &#160; s - 1

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about…

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