6.1 Circular Motion

A car is moving with uniform circular motion and experiences a centripetal force.

The car has mass 500 kg and is travelling around a roundabout with a linear speed of 9 m s⁻¹. The radius of the roundabout is 12 m.

The car proceeds to another roundabout which has radius 20 m. The angular speed of the car at this roundabout is 0.2 rad s^−1.

At this second roundabout, the car is travelling at the maximum speed possible before it would skid. The coefficient of static friction determines the maximum speed possible and is given by , where is the angular speed, r is the radius of the roundabout,  and g is the acceleration due to gravity.

A planet orbits a star in 260 Earth days, which is 22 464 000 s. 

The linear speed of the planet is 35 000 m s⁻¹.

The planet has a mass of 2.7 × 10²⁴ kg and stays in orbit due to a centripetal force.

The planet experiences a centripetal acceleration.

A fairground ride is moving with uniform circular motion. 

A child on the ride has an angular displacement of rad and angular speed of 0.3 rad s⁻¹.

The radius of the ride is 8 m and the child's mass is 35 kg.

The diagram shows the bath of a ball with two forces acting on it. The ball is attached to a string and is swung in a circle in a vertical plane. Air resistance is negligible.

(i)

Label the forces marked on the diagram below:

The centripetal force on the ball is not constant as the ball travels along its circular path.

The radius of the circle is 0.8 m, the mass of the ball is 0.5 kg and the linear velocity is 2.4 m s⁻¹.

The speed and acceleration of the ball varies as it moves around its circular path.