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2.9Force and Translational Dynamics

Circular Motion — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 11 parts Lesson 36 of 36 1 quiz

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Lesson summary

2.9 Circular Motion — AP PHYSICS 1 notes: Describe motion in a circle using centripetal acceleration, period, frequency and the forces that provide the centripetal force.Uniform circular motion = motion in a circle at constant speed.Velocity — tangent to the circle and at right a…

  • No centrifugal force
  • Net inward force
  • Not a new force
  • Force removed
  • Minimum speed at top
  • Gravity supplies the force

Section 1 of 11Uniform circular motion

Uniform circular motion
Uniform circular motion motion in a circle at constant speed.
Velocity
  • Velocity tangent to the circle and at right angles to the radius; its direction changes continuously.
Acceleration
  • Acceleration the object accelerates even at constant speed because the velocity direction changes.
No centrifugal force
  • No centrifugal force in an inertial frame the outward feeling is inertia.

Section 2 of 11Period and frequency

T = 1/f
What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)
  • T = period, the time for one revolution (s); f = frequency, revolutions per second (Hz).
v
2πr/T
What the symbols mean: v = speed (m s−1) · ω = angular speed (rad s−1) · r = radius (m) · T = period (s)
  • speed equals circumference divided by period.

Section 3 of 11Centripetal acceleration and force

ac
ac v2/r
  • directed toward the centre of the circle.
Net inward force
  • ΣFtoward centre = mv2/r.
Not a new force
  • Not a new force centripetal force is the role played by real forces.
    • (tension, gravity, friction, normal force or their components)
Force removed
  • Force removed the object leaves along the tangent, not radially outward.
    • (Newton's first law)

Section 4 of 11What supplies the centripetal force

SituationForceEquation
Car on flat bendStatic frictionμmg = mv2/r at the limit
Satellite or MoonGravityGMm/r2 = mv2/r
Ball on a stringTension (component)T = mv2/r
Top of vertical loopNormal force + weightN + mg = mv2/r
Bottom of vertical loopNormal force − weightN − mg = mv2/r

Section 5 of 11Vertical circles

Top
  • FN + mg = mv2/r.
Bottom
  • FN − mg = mv2/r.
Minimum speed at top
  • Minimum speed at top gravity alone supplies the centripetal force, giving v = √(gr).

Section 6 of 11Circular orbits

Circular orbits
Gravity supplies the force
  • GMm/r2 = mv2/r, so v = √(GM/r).
Mass independence
  • Mass independence the orbital speed does not depend on the satellite's mass.
Period and radius
  • Period and radius related to the mass of the central body.
    • (Kepler's third law)

Section 7 of 11Changing speed

Tangential acceleration
Tangential acceleration rate of change of speed, directed along the tangent.
Net acceleration
  • Net acceleration vector sum of centripetal and tangential components.

Section 8 of 11Solving circular-motion problems

1
Identify the centre of the circle and the radius.
2
Draw a free-body diagram at the point of interest.
3
Take the direction toward the centre as positive.
4
Write ΣFtoward centre = mv2/r.
5
Solve for the unknown speed, force or radius.

Section 9 of 11More from the specification

More from the specification
Conical pendulum
  • Mass on a string moving in a horizontal circle
Horizontal component
  • F cos θ for an angle θ to the horizontal.
Reaction force
  • Force from a support pushing up on an object.
Linear
  • A graph that is a straight line through the origin, so resistance is constant.
Pendulum
  • A weight swinging on a string, exchanging GPE and KE.
Gravitational force
  • Attractive force between masses.

Section 10 of 11Key terms

TermMeaning
Uniform circular motionMotion in a circle at constant speed.
Centripetal accelerationac = v2/r toward the centre.
Centripetal forceNet force toward the centre, mv2/r.
PeriodTime for one revolution.
FrequencyRevolutions per second, f = 1/T.
Tangential accelerationRate of change of speed along the tangent.

Section 11 of 11Exam technique

1
Drawing a centripetal force as an extra force on the diagram — it is the net of the real forces.
2
Thinking the object flies outward when the string breaks — it moves along the tangent.
3
Saying there is no acceleration at constant speed — velocity direction changes.
4
Using the wrong sign for the normal force at the top and bottom of a loop.

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