Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 390

Inertia

Is inertia solely dependent on mass?

This is what I’m hearing, and I pretty much accept it, but I’m wondering why it isn’t also dependent on velocity.

Example.

We want to stop a 100kg trolley with a constant v of 6m/s in 2s;
F=ma
F=100kg(-3m/s/s)
F=-300N

Compared with the same trolley with a constant v of 12m/s (again, stopping it in 2s);
F=ma
F=100kg(-6m/s/s)
F=-600N

**

So it takes more F to stop the trolley when it’s moving faster. Why doesn’t this translate to; the trolley’s tendency to resist acceleration depends on, among other things, the trolley’s velocity?

---

Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,717

Re: Inertia

Usually I can answer your questions based on what I was taught and passed on in my own teaching.  This one is the exception. In all the Newtonian mechanics and physics questions I have encountered, inertia has never occurred.

I had to go up in my loft and get down all my old texts on applied maths and physics.  Some just refer to Newton and  basically say bodies possess the property of inertia, that is they do not accelerate unless acted upon by an external force. 

I also tried googling the units for inertia. I got two answers:

Mass is a measure of an object's inertia. The more mass an object has, the more inertia it has.

The SI unit for inertia is kilogram-meter squared (kg⋅m²). While the term "inertia" is often used to refer to an object's resistance to changes in motion, the actual concept of resistance to change is often referred to as moment of inertia. The moment of inertia is a measure of how an object resists rotational acceleration.

The first is inertia as it applies to linear motion and the second to rotating objects. 

The measure of linear kinetic energy is 1/5 . m . v^2 and for rotating objects 1/2 . I / w^2 where I is the moment of inertia and w the angular velocity.

We're not the only ones confused. Have a look at this thread :

https://physics.stackexchange.com/quest … n-stopping

So there we are. Everyone is confused and there's no one answer.

LATER EDIT: I've given this some over-night thought.  For an object with zero or uniform velocity it's inertia is because of its mass.  More mass, more inertia.  It's actual velocity is irrelevant.  The Earth rotates on its axis, and around the Sun, which in turn, rotates around the centre of the Galaxy, which is moving relative to other galaxies.  That's why we have the concept of frames of reference.

If you consider that trolley going at various speeds, then, yes, the amount of force to reduce that velocity to zero will vary, but that doesn't alter its inertia. It just gives you the means to do the calculation.  If you set up a frame of reference that travels at 6 m/s in the second case, then the trolley is only travelling at 6 m/s relative to that frame and so can be 'brought to rest' in the frame with the same effort as the first case.

Momentum gives you a way to measure the force required, but I showed in a previous post that impulse is just a way of applying v = u + at to determine F.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob