Horizontal Circular Motion

• An example of horizontal circular motion is a vehicle driving on a curved road
• The forces acting on the vehicle are:
  • The?friction?between the tyres and the road
  • The?weight?of the vehicle downwards
• In this case, the centripetal force required to make this turn is provided by the frictional force
  • This is because the force of friction acts towards the centre of the circular path
• Since the centripetal force is provided by the force of friction, the following equation can be written:

• Where:
  • m?= mass of the vehicle (kg)
  • v?= speed of the vehicle (m s^–1)
  • r?= radius of the circular path (m)
  • μ =?static coefficient of friction
  • g?= acceleration due to gravity (m s^–2)

• Rearranging this equation for?v?gives:

v²?= μgr

• This expression gives the maximum speed at which the vehicle can travel around the curved road without skidding
  • If the speed exceeds this, then the vehicle is likely to skid
  • This is because the centripetal force required to keep the car in a circular path could not be provided by friction, as it would be too large

• Therefore, in order for a vehicle to avoid skidding on a curved road of radius?r, its speed must satisfy the equation

Banking

• A banked road, or track, is a curved surface where the outer edge is raised higher than the inner edge
  • The purpose of this is to make it safer for vehicles to travel on the curved road, or track, at a reasonable speed without skidding
• When a road is banked, the centripetal force no longer depends on the friction between the tyres and the road
• Instead, the centripetal force depends solely on the normal force and the weight of the vehicle

Vertical Circular Motion

• An example of vertical circular motion is swinging a ball on a string in a vertical circle
• The forces acting on the ball are:
  • The?tension?in the string
  • The?weight?of the ball downwards

• As the ball moves around the circle, the?direction?of the tension will change continuously
• The?magnitude?of the tension will also vary continuously, reaching a?maximum?value at the?bottom?and a?minimum?value at the?top
  • This is because the direction of the weight of the ball never changes, so the resultant force will vary depending on the position of the ball in the circle

• At the bottom of the circle, the tension must overcome the weight, this can be written as:

• As a result, the acceleration, and hence, the?speed?of the ball will be?slower?at the top
• At the top of the circle, the tension and weight act in the same direction, this can be written as:

• As a result, the acceleration, and hence, the?speed?of the ball will be?faster?at the bottom