Circular Motion

What is the equation for critical speed for circular motion in a vertical plane?

v = √(gr)

Critical speed = √(acceleration of free fall × radius)

How do you derive equation for critical speed for circular motion in a vertical plane?

W=mv²/r

mg=mv²/r

g=v²/r

v²=gr

v=√(gr)

For circular motion in a vertical plane, what is the centripetal force equal to at the critical velocity?

The weight is equal to the centripetal force

Why are some sharp bends in the road are banked?

• When a vehicle rounds a bend on a flat road, the centripetal force required is provided by friction between the tyres and the road. The friction available on a flat corner determines how fast the corner can be ‘taken’.

• The sharper the bend, the smaller the radius and the greater the centripetal force which needs to be provided for the car to follow the bend.

• If friction is not enough additional centripetal force can be provided by banking the road so that the horizontal component of the Normal Contact force acts towards the centre of the bend.

Why do aeroplanes bank their wings to turn?

When 𝜃 is the angle of banking

• The horizontal component of the lift 𝐿𝑠𝑖𝑛𝜃 is unbalanced and provides a centripetal force so the plane will follow a horizontal circular path.

• The vertical component 𝐿𝑐𝑜𝑠𝜃 is balanced by the weight.

Define the centripetal force

A force that keeps a body moving with constant speed in a circular path