12.2.1 Centripetal Acceleration

• Velocity and acceleration  are both vector  quantities
• An object in uniform circular motion is continuously changing direction, and therefore is constantly changing velocity
  • The object must therefore be accelerating

• This is called the centripetal acceleration and is perpendicular to the direction of the linear speed
  • Centripetal means it acts towards the centre of the circular path

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

• The centripetal acceleration is caused by a centripetal force of constant magnitude that also acts perpendicular to the direction of motion (towards the centre)
• Therefore, the centripetal acceleration and force act in the same direction

• 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