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2.8.4Force and Translational Dynamics

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

5 min read 9 parts Lesson 34 of 36 1 quiz

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Lesson summary

2.8.4 Circular Motion Examples — AP PHYSICS 1 notes: Identify which force supplies the centripetal force in common situations, including banked surfaces, and solve typical problems.Identify the object and its circular path and mark the centre.Draw all real forces on the object.Ch…

  • Car on a flat bend
  • Ball on a string on a smooth table
  • Coin on a turntable
  • Rider in a spinning drum
  • Forces with friction
  • Net centripetal force

Part 1 of 7Strategy for any situation

1
Identify the object and its circular path and mark the centre.
2
Draw all real forces on the object.
3
Choose a radial axis toward the centre and a perpendicular axis (vertical for a horizontal circle).
4
Resolve forces; vertical forces usually cancel for a horizontal circle.
5
Set the net radial force equal to mv2/r (or 4π2mr/T2) and solve.
Check
  • Check name the object that exerts the inward force; if none can be named there is an error.
Units
  • Units convert km/h to m/s by dividing by 3.6.

Part 2 of 7Flat curves, strings and turntables

1Car on a flat bend
  • Car on a flat bend static friction toward the centre is the only horizontal force, so fs = mv2/r and N = mg.
  • At the limit μsmg = mv2/r, so vmax = √(μsgr).
  • Ice or rain lowers μs and the safe speed.
2Ball on a string on a smooth table
  • Ball on a string on a smooth table tension is the only horizontal force: T = mv2/r.
3Coin on a turntable
  • Coin on a turntable it stays while mv2/r ≤ μsmg, so coins at larger r slip first.
4Rider in a spinning drum
  • Rider in a spinning drum the wall normal force provides mv2/r while wall friction balances weight, so the rider stays if μsN ≥ mg.

Part 3 of 7Banked surfaces

Banked surface
  • Banked surface a curved road or track whose outer edge is raised higher than the inner edge.
Purpose
  • Purpose lets vehicles take the curve at reasonable speed without skidding;
    • steeper banking allows higher speed.
Forces with friction
  • Forces with friction weight down, normal force perpendicular to the surface, friction parallel to the surface.
    • (up or down the slope)
Net centripetal force
  • Net centripetal force the net horizontal force toward the centre of the circle, made from horizontal components of N and friction.
Static or kinetic
  • Static or kinetic static friction acts if the tyre rolls; kinetic friction acts if the vehicle skids.

Part 4 of 7Banked speeds

CaseFriction directionCentripetal force
Faster than ideal speedStatic friction down the slope (prevents skidding upward)Fc = FNsinθ + Ff,scosθ
Slower than ideal speedStatic friction up the slope (prevents skidding downward)Fc = FNsinθ − Ff,scosθ
Ideal banking (no friction)NoneFc = FNsinθ
Ideal banking
  • FNcosθ = mg and FNsinθ = mv2/r, so tanθ = v2/(gr).
Example
  • Example v = 40 m/s and r = 100 m need θ about 58°.

Part 5 of 7Hills and dips

Crest of a hill
  • Crest of a hill centre below: mg − N = mv2/r, so N = m(g − v2/r).
  • N is less than the weight and falls as speed rises.
  • At v = √(gr), N = 0 and the wheels just leave the road.
Dip
  • Dip centre above: N − mg = mv2/r, so N exceeds the weight, compressing the suspension.

Part 6 of 7Satellites and planets

Circular orbit
  • GMm/r2 = mv2/r, so v = √(GM/r).
Astronauts
  • Astronauts are in free fall, not beyond gravity.
Geostationary satellite
  • Geostationary satellite orbit period 24 h above the equator so it stays over one point.

Part 7 of 7More from the specification

1Gravitational force
  • Attractive force between masses.
2Conical pendulum
  • Mass on a string moving in a horizontal circle
3Minimum speed
  • Smallest top speed that keeps contact, √(gr).
4Reaction force
  • Force from a support pushing up on an object.
5Acceleration
  • Rate of change of velocity.
6Radius
  • Distance from the centre to the circular path.
7Linear
  • A graph that is a straight line through the origin, so resistance is constant.
8Uniform
  • Same density throughout, so the weight acts at the centre.
9Pendulum
  • A weight swinging on a string, exchanging GPE and KE.
10Frequency
  • Revolutions per second, f = 1/T.
    What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)
11Constant
  • Not changing.
12Centripetal acceleration
  • Ac = v2/r toward the centre.

Key terms

TermMeaning
Flat curveHorizontal circular bend without banking.
Banked curveCurve with the outer edge raised so N has an inward component.
Static frictionFriction preventing the tyre sliding on the road.
Orbital speedSpeed of a satellite in circular orbit.
Geostationary orbit24 h equatorial orbit above a fixed point on Earth.

Avoid these mistakes

1
Not naming the force that provides the centripetal force.
2
Using kinetic friction for a car turning without skidding.
3
Putting centrifugal force in the diagram.
4
Using the wrong sign for the weight term on a crest versus a dip.
5
Using the diameter instead of the radius.

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