## Inertia in Linear and Rotational motion?

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Boris Lagutin

### Inertia in Linear and Rotational motion?

Moment of Inertia is drastically applied in Rotational motion. For example, Angular momentum = Moment of Inertia times Angular velocity = Iw. Everywhere, if I don't mistake, Moment of Inertia is used in Rotational motion, including Rotational kinetic energy (KE): KE = 1/2 * I * w(omega). However, Moment of Inertia is not applied in Linear motion at all, if I don't mistake. If it is so, why isn't Moment of Inertia applied in Linear motion?

P.S. I think Inertia plays some role in Linear motion as well as in Rotational motion but Inertia is no any means taken into account in Linear motion formulas (Kinetic energy, momentum etc.). Why does it happen so?

P.P.S. What if define any mass by Inertia, not how it does now Inertia by mass? In other words, change a general method to model systems. Just thoughts.

Thanks a lot.
Last edited by Boris Lagutin on Wed Apr 15, 2015 6:33 am, edited 1 time in total.
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

What if make Inertia as a base for any mass?

thanks.
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

What if Inertia is relative? Maybe it should be related to Special Theory of Relativity?

thanks a lot.
joe
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Location: Sydney

### Re: Inertia in Linear and Rotational motion?

2.
What if define any mass by Inertia, not how it does now Inertia by mass?
You'll notice that I try to avoid using 'inertia' except in 'moment of inertia'. The meaning of inertia is not unanimous. Wikipedia says "Inertia is the resistance of any physical object to any change in its state of motion, including changes to its speed and direction" and "Inertia is one of the primary manifestations of mass".
Mass is what resists acceleration in linear motion
Moment of Inertia is what resists angular acceleration.[/quote]
3.
What if Inertia is relative?
The special theory of relativity (section relativistic mechanics) does consider how Newton's 2nd law transforms between reference frames. Try
http://newt.phys.unsw.edu.au/einsteinli ... namics.htm
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Inertia in Linear and Rotational motion?

joe wrote:1.
Inertia is no any means taken into account in Linear motion formulas (Kinetic energy, momentum etc.). Why does it happen so?
Applying Newton's second law to rotating objects results in
torque = I*angular acceleration
Calculating the kinetic energy due to rotation gives
K = 1/2 I omega^2
If there is no angular acceleration, then the (total) torque is zero.
When there is no angular acceleration, you don't need the moment of inertia.
Instead, you need mass (which some people call linear inertia)

More on next post
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

Moment of Inertia, as I was explained, is treated by some to be mass itself in Linear motion. This claim seems to be doubtful for me so I see some difference (special) in Moment of Inertia in Rotational motion and and Inertia in Linear motion. I intuitively feel that there is something wrong in this point. Nature of this natural occurrence is obscure for me. I feel some kind of element of relativity here, but such relativity which may be not related to high speed... just thoughts

P.S. I somehow relate my intuitive thoughts described above with natural occurrence happening when mass becomes weightless on the top of the vertical rotation of Ferry Wheel. I feel that there is something special here about Mass, Inertia and Gravity. Now I cannot express them in a scientific logic way. I hope later possibly if I happen not to mistake in my understanding of these physical conceptions.
Last edited by Boris Lagutin on Thu Apr 16, 2015 6:18 am, edited 2 times in total.
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

P.P.S. What if Gravity may be treated as one of kinds of Inertia? Ok. I stop my imagination for a while ... continue later when I will be better ready.

thanks.
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

Just little bit more of my thoughts... My one more claim is that Inertia is relative and that changes in the same system properties may be caused Relativity of its Inertia. Hmm... What if Inertia could be separate from mass? I mean that whether there may be cases in which Inertia could exist dependently from any mass? .... Just thoughts

thanks.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Inertia in Linear and Rotational motion?

Moment of Inertia, as I was explained, is treated by some to be mass itself in Linear motion.
This is confused. See the real definition, with explanation, at
http://www.animations.physics.unsw.edu. ... ation.html

As I've said before, there is an interesting question about inertia and gravity.
Newton's second law: F = m_i * a
Newton's gravity: F_g = m_g * g
Experimentally, we find that gravitational mass m_g and inertial mass m_i are proportional. Therefore, by choice of units, we make them the same and call them both mass, m.
However, there is no simple reason why they have to be proportional.

I've explained this here:
http://www.animations.physics.unsw.edu. ... y.htm#Mach
http://www.animations.physics.unsw.edu. ... wton.htm#m

Joe
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

Thank you very much, Joe.

Now I need to do some physics studies and then I will return to this stuff (it's difficult for me to do different physics things at the same time, now I must learn waves, sound). I cannot penetrate the stuff discussed here well without more or less deeply researching it. So I need to get a good moment to think of and understand all of that well.

P.S. Truly saying, the discussions with you help me pretty much because of that I post my ideas here.

Have a nice day
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Inertia in Linear and Rotational motion?

now I must learn waves, sound
Then have a look at:
http://www.animations.physics.unsw.edu.au/waves-sound/
and perhaps even our lab's outreach site:
http://newt.phys.unsw.edu.au/music/

Joe
Boris Lagutin

### Re: Inertia in Linear and Rotational motion?

Let me return to circular motion of an object. We have a centripetal acceleration towards a circle motion center and also we have a tangent velocity which is perpendicular to the acceleration vector. As known, a net force is at the same direction as that the acceleration is at. In this case, a net force is towards the center of the circular motion. I don't talk of angular momentum here. We can say that the object has angular momentum but to get momentum one first needs to apply a force, right?

Question: What makes the object go at the tangent direction (tangent velocity direction) after being released?

Thank you.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Inertia in Linear and Rotational motion?

The angular momentum L = r X p = r X mv
where the vector cross product is defined here
http://www.animations.physics.unsw.edu. ... .htm#cross
if you need it.

Note that L depends on which origin one uses, though of course for circular motion one usually chooses the center of the circle.
Note also that an object travelling in a straight line that doesn't go through the origin has a non-zero L. So an object with zero acceleration (i.e. subject to no nett force) can have both linear and angular momentum.

See
http://www.animations.physics.unsw.edu. ... tion.htm#L
for angular momentum.

Joe
joe
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Joined: Fri Aug 29, 2003 11:57 am
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