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2.8.1Force and Translational Dynamics

Uniform Circular Motion — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 31 of 36 1 quiz

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Lesson summary

2.8.1 Uniform Circular Motion — AP PHYSICS 1 notes: Describe uniform circular motion using period, frequency and speed, and explain why a net force toward the centre is needed.Uniform circular motion = travel around a circle at constant linear speed.Velocity — tangent to the circ…

  • Acceleration
  • Frequency f
  • What the symbols mean
  • Rigid rotating body
  • Two quantities fix the third
  • Newton's first law

Part 1 of 7Uniform circular motion

Uniform circular motion
Uniform circular motion travel around a circle at constant linear speed.
Velocity
  • Velocity tangent to the circle and at right angles to the radius, so its direction changes continuously.
Acceleration
  • Acceleration the object accelerates even though its speed is constant.
Examples
  • Examples a car on a curve at steady speed, a ball whirled on a string, the Moon around Earth, a point on a wheel rim.

Part 2 of 7Period, frequency and speed

Period, frequency and speed
Period T
Period T time for one complete revolution, in s.
Frequency f
Frequency f revolutions per second, in Hz (s−1), with f = 1/T.
Speed
  • Speed v = 2πr/T = 2πrf,
  • because one revolution covers the circumference 2πr in time T.
    What the symbols mean: v = speed (m s−1) · ω = angular speed (rad s−1) · r = radius (m) · T = period (s)
  • Derivation uses average speed = total distance / total time.
Rigid rotating body
  • Rigid rotating body every point has the same T and f, but a point at twice the radius has twice the speed.
Two quantities fix the third
  • Two quantities fix the third any two of v, r and T determine the other.

Part 3 of 7Why a net force is needed

1Newton's first law
  • Newton's first law with no net force an object moves in a straight line at constant velocity.
2Centripetal force
Centripetal force the net force toward the centre, needed to keep changing the velocity direction.
  • It is not a new kind of force.
  • It is supplied by tension, friction, gravity, a normal force or a combination.
3No work
  • No work it is perpendicular to the velocity so it changes direction but not speed.
4If it vanishes
  • If it vanishes the object moves off along the tangent at its existing speed, not radially outward.

Part 4 of 7No centrifugal force

Inertial frame
  • Inertial frame there is no outward centrifugal force.
Outward sensation
  • Outward sensation the passenger tends to continue in a straight line while the car turns.
Free-body diagram
  • Free-body diagram show only real forces, then set the components toward the centre equal to mv2/r.

Part 5 of 7Speed, velocity and graphs

Speed, velocity and graphs
Average velocity over one revolution
  • Average velocity over one revolution zero because the displacement is zero.
Average speed
  • 2πr/T.
Speed–time graph
  • Speed–time graph a horizontal line.
Position component against time
  • Position component against time sinusoidal, linking to simple harmonic motion.
Scaling
  • Scaling doubling f at fixed r doubles v; doubling r at fixed T doubles v.

Part 6 of 7Unit checks

Units
  • Units period in s and radius in m.
rpm
  • rpm divide revolutions per minute by 60 to get Hz, so 120 rpm = 2.0 Hz and T = 0.50 s.

Part 7 of 7More from the specification

1Pendulum
  • A weight swinging on a string, exchanging GPE and KE.
2Gravitational force
  • Attractive force between masses.
3Static friction
  • Friction between surfaces at rest relative to each other; fs ≤ μsFN.
4Conical pendulum
  • Mass on a string moving in a horizontal circle
5Minimum speed
  • Smallest top speed that keeps contact, √(gr).
6Orbital period
  • Time for one orbit.
7Vertical circle
  • Circular motion in a vertical plane, in which gravity does work
8Reaction force
  • Force from a support pushing up on an object.

Key terms

TermMeaning
Uniform circular motionMotion in a circle at constant speed.
Period TTime for one revolution, in s.
Frequency fRevolutions per second, in Hz.
Centripetal forceNet force toward the centre of the circle.
TangentLine touching a circle at a point, in the direction of velocity.
CircumferenceDistance around a circle, 2πr.

Avoid these mistakes

1
Saying constant speed means zero acceleration — the velocity direction changes.
2
Drawing an outward centrifugal force on the free-body diagram.
3
Saying a released object flies radially outward — it moves along the tangent.
4
Mixing up period and frequency.
5
Believing centripetal force is an extra force added to the others.

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