Circular Motion

A particle completes one full revolution of a circle in 4 seconds. Find its angular velocity.

A particle moves on a circle of radius 0.5 m with an angular velocity of 4 rad/s. Find its linear speed.

A particle moves in a circle of radius 2 m with a constant speed of 10 m/s. Find its centripetal acceleration.

A particle moves in a circle of radius 2 m with angular velocity 5 rad/s. Find its centripetal acceleration.

A fan rotates at a frequency of 2 Hz. What is its angular velocity?

A 2 kg stone tied to a string moves in a circle of radius 1 m with speed 4 m/s. Find the tension needed in the string (assume the circle is horizontal and on a frictionless surface, so tension alone provides the centripetal force).

A car negotiates a curve of radius 40 m banked at an angle θ (assume no friction). If its speed is 20 m/s, find tanθ. (g = 10 m/s²)

A car can safely negotiate a flat circular curve of radius 20 m at a maximum speed of 10 m/s. Find the coefficient of static friction between the tyres and the road. (g = 10 m/s²)

A conical pendulum of string length 1 m has its bob moving in a horizontal circle with the string making 60° with the vertical. Find the tension in the string for a 1 kg bob. (g = 10 m/s²)

For the same conical pendulum as above (L = 1 m, θ = 60°), find the speed of the bob. (g = 10 m/s²)

A bucket of water is whirled in a vertical circle of radius 2 m. What is the minimum speed required at the topmost point so that the water does not spill out? (g = 10 m/s²)

A small ball tied to a string of length 2 m is to be swung in a complete vertical circle. Find the minimum speed required at the LOWEST point. (g = 10 m/s²)

A 0.5 kg ball is whirled in a vertical circle of radius 2 m, given exactly the minimum possible speed at the bottom to complete the loop. Find the tension in the string at the lowest point. (g = 10 m/s²)

Using the same setup as above (minimum possible speed for completing the loop), find the tension in the string at the TOPMOST point.

A ball tied to a string of length 1 m is given a speed of 3 m/s at the lowest point. What happens to the ball? (g = 10 m/s²)

A ball tied to a string of length 1 m is given a speed of 6 m/s at the lowest point. What happens to the ball? (g = 10 m/s²)

A particle moves on a circle of radius 4 m. Its speed at time t is given by v = 2t² (in m/s, t in seconds). Find its tangential acceleration at t = 2 s.

For the same particle as above (v = 2t², r = 4 m), find its centripetal acceleration at t = 2 s.

A wheel starts from rest and gains a constant angular acceleration of 4 rad/s². Find its angular velocity after 5 seconds.

For the same wheel as above (starting from rest, α = 4 rad/s²), find the total angular displacement after 5 seconds.