Non-Uniform Circular Motion (DP IB Physics): Revision Note

Non-Uniform Circular Motion

• Some bodies are in non-uniform circular motion

• This happens when there is a changing resultant force such as in a vertical circle

• 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