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Circular Motion in Physics

A body going round a circle at a steady speed is still accelerating, and that is the whole difficulty of this topic. The speed never changes but the direction does, so there is always an acceleration pointing at the centre, and something has to supply it. The blocks open with that demand on real situations, a conical pendulum, a banked bend, a car on a flat curve, then allow the speed itself to change so that a second acceleration appears along the tangent, and finish with the view from inside a frame that is itself accelerating, where the books seem to balance only once a pseudo force is added.

Tension in the string of a conical pendulum

Given

  • (kg)
  • (rad)

Constant used

Period of a conical pendulum

Given

  • (m)
  • (rad)

Constant used

Greatest safe speed round a level curve

Given

  • (m)

Constant used

Correct speed round a frictionless banked curve

Given

  • (m)
  • (rad)

Constant used

Banking angle for a given design speed

Given

  • (m/s)
  • (m)

Constant used

Tension at the lowest point of a vertical circle

Given

  • (kg)
  • (m/s)
  • (m)

Constant used

Tension at the highest point of a vertical circle

Given

  • (kg)
  • (m/s)
  • (m)

Constant used

Least speed at the highest point to stay on the circle

Given

  • (m)

Constant used

Least speed at the lowest point to complete a vertical circle

Given

  • (m)

Constant used

Angular acceleration

Given

Tangential acceleration from the angular acceleration

Given

  • (m)
  • (rad/s²)
Angular speed after a time

Given

  • (rad/s)
  • (rad/s²)
  • (s)
Angular displacement after a time

Given

  • (rad/s)
  • (rad/s²)
  • (s)
Angular speed from the angular displacement, without the time

Given

  • (rad/s)
  • (rad/s²)
  • (rad)
Radial acceleration when the speed is changing

Given

  • (m/s)
  • (m)
  • (rad/s)
Total acceleration in nonuniform circular motion

Given

  • (m/s)
  • (m)
  • (m/s²)
Direction of the total acceleration

Given

  • (m/s²)
  • (m/s²)
Pseudo force in a frame accelerating in a straight line

Given

  • (kg)
  • (m/s²)
Centrifugal force in a rotating frame

Given

  • (kg)
  • (rad/s)
  • (m)
Newton's second law as seen from an accelerating frame

Given

  • (m/s²)
  • (m/s²)