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2.5.8Force and Translational Dynamics

Inertial vs Gravitational Mass — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 21 of 36 1 quiz

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2.5.8 Inertial vs Gravitational Mass — AP PHYSICS 1 notes: Distinguish inertial mass from gravitational mass and explain why they are experimentally equal.Inertial mass = the property that determines how strongly an object resists changes in its motion (inertia).Newton's second l…

  • Newton's second law
  • Mass–spring method
  • Force-sensor method
  • Law of gravitation
  • Balance scale
  • Spring scale or force sensor

Section 1 of 9Inertial mass

Inertial mass
Inertial mass the property that determines how strongly an object resists changes in its motion (inertia).
Newton's second law
  • Newton's second law defines it through msys = Fnet / asys.
  • A larger inertial mass needs a larger net force for the same acceleration.

Section 2 of 9Measuring inertial mass

Principle
  • Principle the object is accelerated by a known force and its response is measured.
Mass–spring method
  • Mass–spring method the object oscillates on a spring of known spring constant k and its period T is timed.
  • Set the mass oscillating and time 10 oscillations with a stopwatch.
  • Divide the total time by 10 to obtain the period T (one full oscillation).
  • The period gives the inertial mass through msys = kT2 / 4π2.
Force-sensor method
  • Force-sensor method pulling a cart with a force sensor and measuring a with a motion sensor gives m = F / a.

Section 3 of 9Gravitational mass

Gravitational mass
Gravitational mass the property that sets the size of the gravitational force an object feels and exerts.
Law of gravitation
  • Fg = G m1m2 / r2 and W = mg both contain gravitational mass.
  • A larger gravitational mass gives a larger gravitational force in the same field.

Section 4 of 9Measuring gravitational mass

1Principle
  • Principle the object is placed in a gravitational field and the gravitational force on it is compared with a standard.
2Balance scale
  • Balance scale the standard masses needed to hold the scale horizontally on its pivot equal the gravitational mass.
3Spring scale or force sensor
  • Spring scale or force sensor the reading divided by g gives the gravitational mass.
4Independent physics
  • Independent physics the two procedures rely on different laws.
    • (Newton's second law versus gravitation)

Section 5 of 9Equivalence principle

1Experimental result
  • Experimental result inertial and gravitational mass of an object are found to be equal to extremely high precision.
2Algebra
  • Algebra setting Fnet = msysasys equal to G m1m2 / r2 with msys = m1 gives asys = G m2 / r2.
  • The object's own mass cancels, so asys = g.
3Consequence
  • Consequence all objects fall with the same acceleration in the same field, whatever their mass or material.
4If the ratio were not 1
  • If the ratio were not 1 a feather and a hammer would fall at different rates in a vacuum, and they do not.

Section 6 of 9Tests and consequences of the equivalence

1Free-fall test
  • Free-fall test objects of different materials dropped together in a vacuum land together.
2Pendulum test
  • Pendulum test bobs of different material but equal length swing with equal periods.
3Accelerating laboratory
  • Accelerating laboratory a downward pull in a closed lab cannot be distinguished from uniform upward acceleration of the lab.
4Free-falling laboratory
  • Free-falling laboratory behaves like one far from any gravity, which is why orbiting astronauts feel weightless.
5Equal numbers, different ideas
  • Equal numbers, different ideas inertial mass answers how hard it is to accelerate the object;
    • gravitational mass answers how strongly it attracts and is attracted.

Section 7 of 9More from the specification

More from the specification
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.
Resistance
  • Opposition to current, R = V / I, in ohms (Ω).
System
  • Objects analysed together.
Normal
  • Line at 90° to a surface.
Distance
  • Total length of path travelled, a scalar.
Satellite
  • A body that orbits a larger one; the Moon is the Earth's natural satellite.
Apparent weight
  • Normal force on an object.
Field strength
  • G = Fg/m.
Field lines
  • Lines showing the direction and strength of a magnetic field.

Section 8 of 9Key terms

TermMeaning
Inertial massMeasure of resistance to acceleration, m = Fnet / a.
Gravitational massProperty that determines the gravitational force on and from an object.
InertiaProperty that makes an object resist changes in its motion.
Equivalence principleInertial and gravitational masses are equal, so gravity and acceleration effects are indistinguishable locally.
Balance scaleDevice comparing gravitational masses by horizontal balance.

Section 9 of 9Exam technique

1
Thinking inertial and gravitational mass are different numbers for the same object — they are experimentally equal.
2
Saying weight is the measure of inertia — inertia is measured by mass.
3
Explaining equal fall by saying heavier objects have less inertia — the object's mass cancels between gravitational pull and inertia.
4
Believing an object in space has no mass because it has no weight — mass is unchanged.
5
Using a balance to find inertial mass — a balance gives gravitational mass.

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