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2.4.2 Inertial mass

Inertial mass measures resistance to acceleration

Definition

Inertia

Inertia is the tendency of an object to remain at rest or continue moving at constant velocity unless a resultant force acts on it.

Definition

Inertial mass

Inertial mass is the ratio of the resultant force acting on an object to the acceleration it produces, measured in kilograms.

  1. Inertial mass measures how difficult it is to change an object's velocity, including how difficult it is to start an object moving from rest.
  2. The defining equation is m=Fam=\dfrac{F}{a}m=aF​, where mmm is inertial mass in kilograms, FFF is resultant force in newtons and aaa is acceleration in metres per second squared.
  3. A large inertial mass means that the same resultant force produces a smaller acceleration because a=Fma=\dfrac{F}{m}a=mF​.
  4. A small inertial mass means that the same resultant force produces a larger acceleration.

Resultant force must be used

  1. Use the resultant force, not one individual force, because opposing forces may partly or completely cancel.
  2. If the resultant force is zero, the acceleration is zero, so the object remains at rest or continues at constant velocity.
  3. Inertial mass is a property of the object and does not depend on the strength of the gravitational field.
Common Mistake
  • Do not describe inertia as a force because inertia is a tendency, not an interaction acting on the object.
  • Do not use weight in m=Fam=\dfrac{F}{a}m=aF​ unless weight is the resultant force in the situation.
Example
  • Given: a resultant force of 18 N18\ \text{N}18 N produces an acceleration of 3.0 m/s23.0\ \text{m/s}^23.0 m/s2.
  • Rearrange Newton's second law: m=Fam=\dfrac{F}{a}m=aF​.
  • Substitute: m=18 N3.0 m/s2=6.0 kgm=\dfrac{18\ \text{N}}{3.0\ \text{m/s}^2}=6.0\ \text{kg}m=3.0 m/s218 N​=6.0 kg.
  • The object's inertial mass is 6.0 kg6.0\ \text{kg}6.0 kg.

Comparing objects from data

  1. For the same resultant force, compare accelerations using m=Fam=\dfrac{F}{a}m=aF​; the object with the smaller acceleration has the greater inertial mass.
  2. For the same acceleration, the object that requires the larger resultant force has the greater inertial mass.
  3. On a graph of resultant force against acceleration, F=maF=maF=ma, so the gradient equals the inertial mass.
Exam technique
  • When explaining a comparison, link the same force to the different accelerations and then state which object has the greater inertial mass.
  • For calculations, identify the resultant force before substituting and include the unit kg\text{kg}kg.

Force and acceleration data reveal mass

  1. A straight-line graph through the origin shows that resultant force is directly proportional to acceleration when mass is constant.
  2. A steeper FFF against aaa graph represents a larger inertial mass because its gradient ΔFΔa\dfrac{\Delta F}{\Delta a}ΔaΔF​ is larger.
Self review
  • What does inertial mass measure?
  • State the equation that defines inertial mass.
  • Why must resultant force be used in the equation?
  • What does the gradient of a force against acceleration graph represent?
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2.4.2 Inertial mass Revision Guide

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  2. /Physics
  3. /2.4.2 Inertial mass

Revision notes for Edexcel GCSE Physics 2.4.2 Inertial mass: explanations and worked examples.

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