Intertial mass and gravitational mass.

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joe
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Intertial mass and gravitational mass.

Postby joe » Thu Aug 28, 2014 12:34 pm

This thread is redirected from What causes inertia? in the forum of the MOOC, Particles to Planets at https://class.coursera.org/particles2planets-001.

It's a good idea to read http://en.wikipedia.org/wiki/Machs_principle and/or http://en.wikipedia.org/wiki/Principle_of_relativity#General_principle_of_relativity before posting here, so we don't spend too much time on basic ideas and terminology.

Here is one way of putting the question. For a falling object in an inertial frame, we write
Total force = m_i*a = m_g*g = gravitational force on the object.
where m_i is the inertial mass and m_g the gravitational mass.

The first equation is Newton's second law. m_i is the object's reluctance to accelerate under a given force.
The last equation indicates one or other gravitational law. m_g is the property of an object that interacts with a gravitational field.

So, why is m_i proportional to m_g?

Joe

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joe
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Re: Intertial mass and gravitational mass.

Postby joe » Fri Sep 19, 2014 12:20 pm

To make the distinction clear, consider the analogy for an object in (only) an electric field, E
Total force = m_i*a = q*E = electrical force on object.

Compare this with a falling object in an inertial frame:
Total force = m_i*a = m_g*g = gravitational force on object.

We're not surprised that the ratio q/m_i is different for protons and neutrons. I was surprised that the ratio* m_g/m_i seems to be constant for all objects. (As was Newton.) Do a pendulum made of graphite (equal numbers of protons and neutrons) and a similar one made of plastic (many more protons than neutrons) have the same period? Why is the answer yes?

To oversimplify: Mach says it's not a coincidence, and that the two are related. Einstein says m_i and m_g are the same thing.

Joe
* And if they are proportional, we can make them equal with choice of units.


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