A sphere is rotating about a diameter. | vedclass

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(B) When a sphere rotates about a diameter,all particles of the sphere perform circular motion about the axis of rotation.For any particle at a distan

Vedclass · Accepted Answer

The particles on the diameter mentioned above do not have any linear acceleration.

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(B) When a sphere rotates about a diameter,all particles of the sphere perform circular motion about the axis of rotation.For any particle at a distance $r$ from the axis of rotation,the angular velocity $\omega$ is the same for all particles.The linear velocity is given by $v = r\omega$. Since $r$ varies for different particles,the linear speed $v$ is different for different particles.The linear acceleration of a particle in circular motion is given by $a = \sqrt{a_c^2 + a_t^2}$,where $a_c = \omega^2 r$ is centripetal acceleration and $a_t = \alpha r$ is tangential acceleration. For uniform rotation,$\alpha = 0$,so $a = \omega^2 r$.Particles on the axis of rotation (the diameter) have $r = 0$,which means their linear velocity $v = 0$ and their linear acceleration $a = 0$.Therefore,the particles on the diameter do not have any linear acceleration.

$A$ sphere is rotating about a diameter.

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