VERTICAL CIRCULAR MOTION

A cylinder of radius R is rotating about its horizontal axis with constant omega=sqrt((5g)/R) . A block of mass m is kept on the inner surface of the cylinder. Block is moving in vertical circular motion without slipping. co–efficient of friction between block and surface of cylinder is mu . If minimum value of mu for complete vertical circular motion of block is (2sqrt(6))/(3x) then find 'x'.

A cylinder of radius R is rotating about its horizontal axis with constant omega=sqrt((5g)/R) . A block of mass m is kept on the inner surface of the cylinder. Block is moving in vertical circular motion without slipping. co–efficient of friction between block and surface of cylinder is mu . If minimum value of mu for complete vertical circular motion of block is (2sqrt(6))/(3x) then find 'x'.

Assertion A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane. (Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed (u) of ball at the lowest position (ugtsqrt(5gR)) . Reason For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal aceleraion of the ball is independent of speed (u) of ball at the lowest position (ugrsqrt5gR)) .

Assertion A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane. (Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed (u) of ball at the lowest position (ugtsqrt(5gR)) . Reason For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal aceleraion of the ball is independent of speed (u) of ball at the lowest position (ugrsqrt5gR)) .

A observer standing in a cart which has acceleration g on horizontal road is observing vertical circular motion of a pendulum. One end of the pendulum string is at rest at O with respect to the cart. Choose the possible position of minimum speed for the pendulum with respect to car during complete vertical circular motion from the figure given below.

Using the energy conservation, derive the expression for the minimum speeds at different locations along a vertical circular motion controlled by gravity. Also prove that the difference between the extreme tensions (or normal forces) depends only upon the weight of the object.

Largely because of riding in cars, you are used to horizontal circular motion. Vertical circular motion would be a novelty. In this sample problem, such motion seems to defy the gravitational force. In a 1901 circus performance, Allo Dare Devil Diavolo introduced the stunt of riding a bicycle in a loop the loop. Assuming that the loop is a circle with radius R=2.7m, what is the least speed v that Diavolo and hisbicycle could have at the top of the loop to remain in contact with it there?

A block of mass m slides down a smooth vertical circular track. During the motion, the block is in