Periodic Motion

Question 1

What are the two conditions for circular motion and the equation for the centripetal force?

Answer 1

1) The centripetal acceleration must be perpendicular to the velocity and towards the centre of the circle.
2) The velocity of an object in uniform circular motion is tangential to the circle.

F = mv^2/r (where centripetal acceleration a = v^2/r)

Question 2

State the two conditions for simple harmonic motion and the equation that shows these conditions.

Answer 2

1) The acceleration must be proportional to the displacement.
2) Acceleration is always in the opposite direction to the displacement

a = -w^2x (where a is acceleration and x is displacement)

Question 3

Why does an object in circular motion accelerate if the speed does not change?

Answer 3

• acceleration is the rate of change of velocity
• velocity is changing despite the object moving at a constant speed as it’s direction is constantly changing when travelling with circular motion