# Center of Mass and Mass Moment of Inertia

• ACE_99
In summary, ACE_99 is trying to determine the mass and center of mass of a bicycle crank by using masses, springs, and a stopwatch. He is stumped and needs help from others.
ACE_99

## Homework Statement

Using masses, springs a stop watch and ruler, determine the location of the center of mass and mass moment of inertia about an axis passing through the center of mass of a bicycle crank.

## The Attempt at a Solution

I've been staring at this problem for a while now and I have no idea where to start. Any help would be much appreciated. I have included a link with what the bike crank looks like.

http://s429.photobucket.com/albums/qq12/ACE_99_photo/"

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Hi ACE_99!

How about using conservation of energy …

suspend the crank so that it hits the spring.

To start how would you actually use what you are given to find the mass of the object?

Is there more than one way?

Given we often can treat objects as point masses concentrated at their center of mass for some problems can you think of any position dependent effect of mass or weight?

As to moment of inertia... what behavior depends on the moment of inertia (you also have a stop watch).

Given the spring (of which presumably you know the spring constants) you have the ability to invoke various types of (note plural types) oscillatory motion the period of which you can time. What oscillatory motion depends on one of the quantities you wish to find?

tiny-tim said:
Hi ACE_99!

How about using conservation of energy …

suspend the crank so that it hits the spring.

Thanks for replies guys. With your method tiny-tim, I'm still not sure how I could use this to find what I'm looking for. Could you elaborate a bit?

jambaugh said:
To start how would you actually use what you are given to find the mass of the object?

Is there more than one way?

Given we often can treat objects as point masses concentrated at their center of mass for some problems can you think of any position dependent effect of mass or weight?

As to moment of inertia... what behavior depends on the moment of inertia (you also have a stop watch).

Given the spring (of which presumably you know the spring constants) you have the ability to invoke various types of (note plural types) oscillatory motion the period of which you can time. What oscillatory motion depends on one of the quantities you wish to find?

ACE_99 said:
With your method tiny-tim, I'm still not sure how I could use this to find what I'm looking for. Could you elaborate a bit?

Come off it!

You have to do some work!

How would you use conservation of energy (and include the moment of inertia) if the crank hit the spring?

Go through your physics text and look for formulas which depend on the specific quantity you want to find. Can you think of a way to exemplify one of those formulas?

## 1. What is the center of mass?

The center of mass is the point at which the entire mass of an object can be considered to be concentrated. It is the balancing point of an object, where all forces acting on the object can be considered to act.

## 2. How is the center of mass calculated?

The center of mass can be calculated by finding the weighted average position of all the individual particles that make up an object. This can be done using the formula: xcm = (m1x1 + m2x2 + ... +mnxn) / (m1 + m2 + ... + mn), where m represents the mass of each particle and x represents its position.

## 3. What is mass moment of inertia?

Mass moment of inertia is a measure of an object's resistance to rotational motion. It is the sum of the individual particles' mass multiplied by the square of their distance from the axis of rotation.

## 4. How is mass moment of inertia calculated?

The mass moment of inertia can be calculated using the formula: I = ∫r²dm, where r represents the distance from the axis of rotation and dm represents the infinitesimal mass of an element of the object. This integral must be taken over the entire object.

## 5. How are the center of mass and mass moment of inertia related?

The center of mass and mass moment of inertia are related in that the center of mass is the point at which the mass moment of inertia is at its minimum value. This means that the center of mass is the point where the object is most resistant to rotational motion.

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