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2.2.17 Circular motion and changing velocity

Speed and velocity

Definition

Speed

The distance travelled by an object per unit time.

Definition

Velocity

The speed of an object in a stated direction.

  1. Speed is a scalar, so it tells you only how fast an object is moving.
  2. Velocity is a vector, so it tells you how fast an object is moving and in which direction.
  3. Two cars travelling at 13 m/s13\ \text{m/s}13 m/s, one heading north and one heading east, have the same speed but different velocities.
  4. The velocity of an object changes if its speed changes, if its direction changes, or if both change.
  5. This means an object can keep a constant speed while its velocity changes, as long as its direction is changing.

Moving in a circle

Definition

Tangent

A straight line that touches a curve at a single point and has the same gradient as the curve at that point.

  1. An object moving in a circle is always changing the direction in which it travels.
  2. At any instant, the object moves along the tangent to the circle, which is at right angles to the radius at that point.
  3. As the object moves round, the tangent points in a different direction at every point on the circle.
  4. If the object moves at a constant speed, the velocity arrows all have the same length, but each one points in a different direction.
  5. The velocity is therefore continuously changing, even though the speed is not.
  6. A car driving round a roundabout at a steady 10 m/s10\ \text{m/s}10 m/s shows this clearly.
    1. At one point the car is heading east at 10 m/s10\ \text{m/s}10 m/s.
    2. A quarter of the way round, the car is heading north at 10 m/s10\ \text{m/s}10 m/s.
    3. Halfway round, the car is heading west at 10 m/s10\ \text{m/s}10 m/s, which is the opposite velocity to the one it started with.

Acceleration in a circle

Definition

Acceleration

The rate of change of velocity.

  1. Acceleration is the rate of change of velocity, not only the rate of change of speed.
  2. An object moving in a circle at a constant speed has a changing velocity, so it is accelerating all the time.
  3. By Newton's first law, a changing velocity needs a resultant force, so there must be a resultant force on any object moving in a circle.
  4. This resultant force acts towards the centre of the circle, which is why the direction of motion keeps turning inwards.
  5. Different forces provide this inward resultant force in different situations.
    1. For a conker whirled on a string, the tension in the string pulls the conker towards the centre.
    2. For a car on a roundabout, friction between the tyres and the road pushes the car towards the centre.
    3. For a rider on a fairground ride, the normal contact force from the seat or the wall pushes the rider towards the centre.
  6. If the inward force suddenly disappears, the object stops turning and carries on in a straight line along the tangent, as Newton's first law predicts.
    1. If the string of a whirling conker snaps, the conker flies off along the tangent, not outwards along the radius.

An object moving in a circle at a steady speed, with its velocity along the tangent and its acceleration pointing towards the centre of the circle along the radius.

Example

Explaining the changing velocity of a cyclist on a velodrome

  • A cyclist rides round a circular velodrome track at a steady speed of 15 m/s15\ \text{m/s}15 m/s.
  • Velocity is a vector, so it depends on direction as well as speed.
  • As the cyclist moves round the track, the direction of motion changes continuously.
  • So the velocity of the cyclist changes continuously, even though the speed stays at 15 m/s15\ \text{m/s}15 m/s.
  • A changing velocity means the cyclist is accelerating, and the resultant force causing this acts towards the centre of the track.
Example

Following a hammer thrower's hammer

  • A hammer thrower swings a heavy ball on a wire in a horizontal circle at a steady speed.
  • The tension in the wire pulls the ball towards the centre of the circle, so its direction keeps changing.
  • When the thrower lets go, the tension disappears and there is no longer an inward resultant force.
  • The ball then flies off along the tangent to the circle at the point of release.
Common Mistake
  • Do not say that an object moving in a circle at a constant speed has a constant velocity, because its direction is changing.
  • Do not say that an object moving in a circle at a constant speed is not accelerating, because any change in velocity is an acceleration.
  • Do not say that an object flies outwards along the radius when the inward force is removed, because it moves off along the tangent.
Exam technique

Explaining circular motion

  • Start by stating that velocity is a vector, so it has a direction.
  • Then say that the direction of the object changes continuously as it moves round the circle.
  • Conclude that the velocity changes even though the speed is constant, and that the object is therefore accelerating.
  • Avoid writing only "because it is moving in a circle", as this repeats the question without explaining it.
Self review
  • What is the difference between speed and velocity?
  • In which direction does an object moving in a circle travel at any instant?
  • Explain why an object moving in a circle at a constant speed has a changing velocity.
  • In which direction does the resultant force on an object moving in a circle act?
  • Describe what happens to a whirling conker if its string snaps.
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2.2.17 Circular motion and changing velocity Revision Guide

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Revision notes for OCR GCSE Physics 2.2.17 Circular motion and changing velocity: explanations and worked examples.

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