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.
- 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.
- 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.
- A large inertial mass means that the same resultant force produces a smaller acceleration because a=Fma=\dfrac{F}{m}a=mF.
- A small inertial mass means that the same resultant force produces a larger acceleration.
Resultant force must be used
- Use the resultant force, not one individual force, because opposing forces may partly or completely cancel.
- If the resultant force is zero, the acceleration is zero, so the object remains at rest or continues at constant velocity.
- 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
- 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.
- For the same acceleration, the object that requires the larger resultant force has the greater inertial mass.
- 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
- A straight-line graph through the origin shows that resultant force is directly proportional to acceleration when mass is constant.
- 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?