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2.5.1Force and Translational Dynamics

Newton’s Law of Gravitation — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 8 parts Lesson 15 of 36 1 quiz

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Lesson summary

2.5.1 Newton's Law of Gravitation — AP PHYSICS 1 notes: State and apply Newton's law of universal gravitation, including the inverse-square dependence.Statement — the gravitational force is directly proportional to each mass and inversely proportional to the square of the separat…

  • Not for uniform fields
  • Doubling the distance
  • Universal gravitational constant
  • Inverse square law
  • Point mass
  • Acceleration

Part 1 of 6The law

Statement
  • Statement the gravitational force is directly proportional to each mass and inversely proportional to the square of the separation of the centers of mass
Equation
  • Fg = Gm1m2/r2
  • Fg is the magnitude of the force in N.
  • G = 6.67 × 10-11 N m2 kg-2.
  • m1, m2 are the masses in kg and r is the center-to-center distance in m.

Part 2 of 6Applicability

Bodies
  • Bodies planets and moons, because their separation is much greater than their radii
Spheres
  • Spheres a uniform sphere acts as a point mass at its center, so its field matches that of a point mass
Not for uniform fields
  • Not for uniform fields the law is for bodies outside a uniform gravitational field

Part 3 of 6Inverse square law

Relation
  • Fg is proportional to 1/r2
Doubling the distance
  • Doubling the distance force falls to one quarter

Part 4 of 6Calculation

1
Find r = R + h when given a height above a surface.
2
Convert all quantities to SI units.
3
Rearrange the equation for the unknown.
4
Substitute and calculate.

Part 5 of 6Pattern: mass of Earth

Data
  • Data satellite 6500 kg, orbit 2000 km above the surface, force 37 kN, Earth radius 6400 km
Distance
  • Distance r = 6.4 × 106 + 2 × 106 = 8.4 × 106 m
Result
  • M = Fr2/(Gm) = 6.02 × 1024 kg

Part 6 of 6More from the specification

More from the specification
Field strength
  • G = Fg/m.
Field lines
  • Lines showing the direction and strength of a magnetic field.
Reference frame
  • Coordinate system used by an observer.
Buoyant force
  • Upward force equal to the weight of displaced fluid.
Equivalence principle
  • Acceleration and gravity are indistinguishable locally.
Weight
  • Gravitational force on a mass.
Acceleration
  • Rate of change of velocity.
Resistance
  • Opposition to current, R = V / I, in ohms (Ω).
Constant
  • Not changing.
System
  • Objects analysed together.
Normal
  • Line at 90° to a surface.
Accelerating
  • Speeding up.
Apparent weight
  • Normal force on an object.

Key terms

TermMeaning
Universal gravitational constantG = 6.67 × 10-11 N m2 kg-2.
Inverse square lawQuantity proportional to 1/r2.
Point massObject modelled at its center.
Gravitational forceAttractive force between masses.

Avoid these mistakes

Avoid these mistakes
Forgetting to add the planet's radius to the altitude.
Forgetting to square r.
Mixing kilometres and metres.

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