Centripetal Acceleration (Cambridge (CIE) A Level Physics)

What causes centripetal acceleration?

Centripetal force

• A centripetal force of constant magnitude always acts perpendicular to the direction of motion and causes centripetal acceleration

• The centripetal force (F) is defined as:

  The resultant force towards the centre of the circle required to keep a body in uniform circular motion. It is always directed towards the centre of the body's rotation.

• Centripetal force is not a separate force of its own

  • It can be created by different forces depending on the situation, for example gravitational force or tension

Examples of centripetal force

• The centripetal force and acceleration act in the same direction towards the centre of the circle

  • Perpendicular to the direction of the linear speed

• Velocity and acceleration  are both vector  quantities

• An object in uniform circular motion is continuously changing direction, so, therefore, has a constantly changing linear velocity

  • The object is accelerating

Centripetal force and acceleration

Centripetal force and acceleration are always directed towards the centre of the circle

Relating centripetal acceleration & angular speed

• An object travelling in uniform circular motion has centripetal acceleration, yet its angular speed (⍵) is constant

  • This is because speed is a scalar quantity, whilst velocity is a vector quantity

  • Therefore, angular speed is the magnitude (size) component of angular velocity

• Key ideas to remember:

  • Angular speed (magnitude) stays constant, angular velocity (direction) is constantly changing

  • Angular speed does not change with radius, but linear speed does

  • The object’s centripetal acceleration is always directed toward the centre of the circle, and is perpendicular to the object’s velocity at any one time

  • Velocity and acceleration are both defined by a change in direction, not just a change in the magnitude