Circular Motion

A road of radius 90 m is banked at an angle whose tangent is 0.6. The coefficient of friction between tyres and road is 0.25. Find the maximum safe speed. (g = 10 m/s²)

A 1 kg bob moves in a vertical circle of radius 2 m on a string with speed 10 m/s at the lowest point. Find the tension when the string makes 120° with the lowest point.

A conical pendulum has a bob of mass 3 kg, with the string making 60° with the vertical. Find the tension in the string. (g = 10 m/s²)

Two particles move on the same circle of radius 3 m in the SAME rotational sense, one at 9 m/s and the other at 6 m/s. Find the rate at which the angle between them is changing.

A ball on a string of length 2.5 m is given a speed of 12 m/s at the lowest point. Determine its motion. (g = 10 m/s²)

A particle is given a small initial speed of 2 m/s at the very top of a smooth sphere of radius 2 m and slides down the outside. At what angle (from the top) does it lose contact with the sphere? (g = 10 m/s²)

A block on a rotating disc is at a distance of 0.5 m from the centre. The coefficient of friction between block and disc is 0.2. Find the maximum angular speed of the disc before the block slips. (g = 10 m/s²)

A 1 kg bob moves in a vertical circle of radius 2 m with speed 12 m/s at the lowest point. Find the tension in the string at the TOPMOST point. (g = 10 m/s²)

A car negotiates a banked curve of radius 50 m at 20 m/s, exactly at the design speed (no friction needed). Find tanθ for the bank.

A particle moves in a circle of radius 5 m such that its speed increases uniformly from 0 to 10 m/s in 5 seconds. Find its tangential acceleration.

For the particle in the previous question, find its centripetal acceleration at the instant its speed is 10 m/s.

A vertical circular loop of radius 1 m is set up inside a lift accelerating DOWNWARD at 4 m/s². Find the minimum speed needed at the lowest point to complete the loop, as seen by an observer inside the lift. (g = 10 m/s²)