Centripetal Force (Edexcel International A Level (IAL) Physics): Revision Note

Centripetal Force

•  Centripetal force can be calculated using any of the following equations:

$F=\frac{m{v}^{\mathit{2}}}{r}=mr{\omega }^2=mv\omega$

• Where:

  • F = centripetal force (N)

  • v = linear velocity (m s^-1)

  • ⍵ = angular speed (rad s^-1)

  • r = radius of the orbit (m)

Centripetal force is always perpendicular to the direction of travel

• The centripetal force is the resultant force on the object moving in a circle

  • This is particularly important if there are multiple forces on the object, such as weight

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:

$T_{max}=\frac{m{v}^2}{r}+mg$

• 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:

$T_{min}=\frac{m{v}^2}{r}-mg$

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