Circular and rotational motion

NUST NET Physics · Physics · Mechanics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A body moving in a circle is always accelerating towards the centre, so it needs a net inward force, the centripetal force. This is not a new force: it is supplied by tension, friction, gravity or a normal reaction.

Rotation mirrors straight-line motion. Moment of inertia I plays the part of mass, torque the part of force and angular momentum Iω the part of momentum. With no external torque, Iω stays constant.

For a satellite, gravity is the centripetal force. The satellite and everything in it are in free fall together, so objects inside press on nothing and appear weightless, although gravity still acts on them.

Rules to remember

Common mistake

Using the height above the ground as r in orbit formulas. r is measured from the centre of the Earth, so r = R + h.

Worked example

A car takes a level bend of radius 80 m. The coefficient of friction between tyres and road is 0.50. Taking g = 10 m s−2, what is the greatest speed at which it can take the bend without skidding?

  1. Friction supplies the centripetal force: at the limit μmg = mv2/r.
  2. The mass cancels: v2 = μgr = 0.50 × 10 × 80 = 400.
  3. v = √400 = 20.

Answer: 20 m s−1

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