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Theme A — Space, Time and Motion

A.2.17 Centripetal Force — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 28 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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A.2.17 Centripetal Force — IB PHYSICS SL notes: Explain why a resultant force towards the centre is required for circular motion and use F = mv²/r = mω²r in a range of situations.Newton's first law — a body moves in a straight line unless a resultant force acts, so circular motio…

  • Centripetal acceleration
  • Not a new force
  • What the symbols mean
  • From period
  • Proportions
  • Car on a flat curve

Part 1 of 8Why a centripetal force is needed

1Newton's first law
  • Newton's first law a body moves in a straight line unless a resultant force acts, so circular motion needs a resultant force.
2Centripetal acceleration
  • Centripetal acceleration the acceleration is towards the centre and perpendicular to the linear speed.
3Centripetal force
Centripetal force the resultant force perpendicular to the velocity, directed towards the centre, that keeps a body in uniform circular motion.
4Not a new force
  • Not a new force it is the name for the resultant of real forces pointing towards the centre.
  • It can be tension, friction, gravity, the normal force, electrostatic or magnetic force.
  • A free-body diagram should not show an extra "centripetal force" arrow.

Part 2 of 8Equations

Magnitude
  • F = mv2/r = mω2r.
    What the symbols mean: F = centripetal force towards the centre (N) · m = mass (kg) · v = speed (m s−1) · ω = angular speed (rad s−1) · r = radius (m)
  • F is the centripetal force in N, v the linear speed, ω the angular speed and r the radius.
From period
  • F = 4π2mr/T2.
Source
  • Source multiply the acceleration equations from the data booklet by m, because F = ma.
No work
  • No work the force is perpendicular to the velocity, so it does no work and the kinetic energy does not change.
Proportions
  • Proportions doubling the speed at the same radius needs four times the force; halving the radius doubles it.

Part 3 of 8Identifying the source of the force

SituationForce providing the centripetal force
Ball whirled on a stringTension
Car on a flat bendStatic friction between tyres and road
Satellite or planetGravitational attraction, GMm/r2 = mv2/r
Charge in a magnetic fieldMagnetic force, qvB = mv2/r
Passenger on a bendPush of the door or seat inwards

Part 4 of 8Horizontal circular motion

1Car on a flat curve
  • Car on a flat curve friction provides the force, so mv2/r = μmg.
  • Maximum speed without skidding vmax = √(μgr), independent of mass.
  • If the speed exceeds this, friction cannot supply the force and the car skids.
2Mass on a string in a horizontal circle
  • Mass on a string in a horizontal circle the string is always at an angle, never horizontal.
  • Vertical balanceFT cos θ = mg.
  • Horizontal component supplies the centripetal force: FT sin θ = mv2/r.
  • θ is measured from the vertical here; the trigonometric function changes if θ is defined differently.
  • Combining the two gives tan θ = v2/(rg).

Part 5 of 8Banked tracks

Banking
  • Banking the outer edge of the curve is raised above the inner edge to allow a reasonable speed without skidding.
No friction
  • No friction the horizontal component of the normal force alone provides the centripetal force.
  • R sin θ = mv2/r and R cos θ = mg, so tan θ = v2/(rg).
With friction
  • With friction static friction acts up or down the slope and adds to or reduces the centripetal force.

Part 6 of 8Vertical circles

1Top of the circle (string)
  • T + mg = mv2/r, so the tension is smallest.
2Bottom of the circle (string)
  • T − mg = mv2/r, so the tension is largest.
3Minimum speed at the top
  • Minimum speed at the top with T = 0, mg = mv2/r so v = √(gr).
4Top of a hill
  • Top of a hill mg − R = mv2/r, so a car loses contact if v2 ≥ gr.

Part 7 of 8Common misunderstandings

Centrifugal force
  • Centrifugal force it is not a real force in an inertial frame;
    • it describes inertia seen from a rotating frame.
String breaks
  • String breaks the object moves off along the tangent, not radially outwards.
Method
  • Method identify the real forces or components pointing inwards and set their sum equal to mv2/r.
Choosing the form
  • Choosing the form use 4π2mr/T2 for a period, mv2/r for a speed and mω2r for an angular speed.

Part 8 of 8More from the specification

More from the specification
Mechanics of Centripetal Force
  • When a body undergoes uniform circular motion at constant speed, a net inward centripetal force acts perpendicularly to the moving velocity vector, continually altering direction without performing work.
Circular Motion in Vertical Planes
  • At the top of a vertical circular trajectory, both the tension and the object's downward weight act in the same direction toward the centre,
  • while at the bottom tension acts opposite to weight, requiring maximum tension.
    • (T = m*v2/r + mg)
Linear Momentum and Impulse
  • A moving body possesses linear momentum p = mv;
  • when subjected to an impact force during a collision, the impulse acting over duration Delta t equals the change in momentum, taking positive and opposite directions into account.
    • (Delta p = F * Delta t)
Drag in Fluid Dynamics
  • An object traveling through a fluid experiences resistive drag forces acting opposite to its motion vector,
  • which increases with speed until balancing gravitational weight at terminal velocity.
Normal reaction
  • The contact force perpendicular to a surface.
Reaction force
  • Force from a support pushing up on an object.
Fluid resistance
  • Drag force from a fluid opposing motion.
Momentum
  • P = mv, a vector.
Weight
  • Gravitational force on a mass.
Constant
  • Not changing.
Collision
  • Short interaction with large internal forces.
Impulse
  • J = FΔt = Δp.
    What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Buoyancy
  • Another name for upthrust.

Key terms

TermMeaning
Centripetal forceResultant force towards the centre that keeps a body in circular motion
Uniform circular motionMotion in a circle at constant speed
Tangential (linear) speedSpeed along the circular path
BankingRaising the outer edge of a curve so the normal force helps provide the centripetal force
Conical pendulumMass on a string moving in a horizontal circle
Centrifugal forceApparent outward force seen only in a rotating frame

Avoid these mistakes

1
Drawing a separate centripetal force arrow on the diagram — it is the resultant of the real forces.
2
Believing a centrifugal force pushes outwards — the body tends to continue straight.
3
Thinking the object leaves radially when the string breaks — it leaves along the tangent.
4
Forgetting that the force does no work — it is perpendicular to the velocity.
5
Using the diameter instead of the radius — use r.

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