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Forces and Newton's Laws of Motion 4.4 Explaining, with examples, the concept of inertia and comparing inertial mass with gravitational mass

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4.4 The concept of inertia - comparing inertial mass and gravitational mass

What is inertia?

Inertia can be defined as the tendency of an object's motion to remain unchanged

(That does NOT mean an object's motion cannot be changed, but a resultant force of >0 must be applied to change to objects motion and inertia is about the force needed)

If we start by thinking about the implication of Newtons First Law of motion ...

... a resultant force is needed to change the motion of any object.

In other words, unless acted on by a resultant force, anything stationary remains at rest (zero velocity), anything moving keeps moving with the same velocity (same speed and direction).

So we can say the tendency of an object to keep moving with the same velocity is called inertia.

Inertial mass measures an object's resistance to being accelerated by a force (F = ma)

We can measure how difficult it is to change an object's velocity by calculating its inertial mass.

An object's inertial mass is a measure of how difficult it is to change its velocity.

We can do this using the equation from Newton's Second Law of motion (force = mass x acceleration).

F = ma, on rearrangement this gives: m = F/a, and this expression defines inertial mass

so inertial mass (kg) = applied force (N) / acceleration (m/s2)

Another way of looking at the equation is to consider the effect of force on acceleration.

a = F/m, some consequences are ...

as already stated, for a given mass on object's acceleration is proportional to the force applied, but ...

if the same force F is applied to two different masses, the smaller mass, with the smaller inertia, will experience the greater acceleration,

and, if two objects have the same mass, then applying the same force to each object will produce the same acceleration.

Inertia and moving objects

As well as looking at inertia from the point of view of acceleration, think about slowing moving objects down.

If two objects of different masses are moving at the same speed, the object of greater mass will need a bigger force to slow it down (decelerate) due to Newton's second law.

Imagine two cars are moving at the same speed and both drivers take the foot off the accelerator. If the two cars experience the same air resistance and wheel-road friction forces, the car of bigger mass would travel on further before coming to a halt. The bigger the inertial mass, the bigger the force would be needed to bring it to a halt in the same stopping distance as the car with the smaller mass. F = ma, force proportional to mass.

Large objects like cargo ships or high speed trains can take several km to come to a halt.

What is the difference between inertial mass and gravitational mass

Inertial mass measures an object's resistance to acceleration.

Inertial mass = force / acceleration  (m = F / a, from F = ma)

Gravitational mass determines the gravitational attractive force it exerts on another object

mass = weight / gravitational field constant (m = W / g, from W = mg).

BUT, inertial mass and gravitational mass are numerical identical.

Keywords, phrases and learning objectives for Newton's laws of motion and the concept of inertia

Know that inertia can be defined as the tendency of an object's motion to remain unchanged.

Be able to explain with examples the concept of inertia and compare inertial mass with gravitational mass.

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