A very small cube of mass III is placed on the inside of a funnel (see Fig.) rotating about a vertical axis at a constant rate of w revolutions per second. The wall of the funnel makes an angle θ with the horizontal. The coefficient of static friction between cube and funnel is μ s and the center of the cube is at a distance r from the axis of rotation. Find the (a) largest and (b) smallest values of ω for which the cube will not move with respect to the funnel.

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Aditi Chauhan · Answer

(a) Use Newton&rsquo;s second law of motion for the forces along the length of incline surface, and assume smaller angular velocity. Also, the frictional force is given as: (b) The figure below shows the forces on the block when the angular velocity of the funnel is extremely large: Also, the frictional force is given as:

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