# Understanding moment of inertia values

I have done some extensive self study on MOI but I don't understand it's meaning in application.

An example is imagine a stick of butter is dropped on the ground. Now ignoring friction and the other variables we can remove for learning purposes, let's assume the butter stick is kicked and it is gliding along the ground and it isn't rolling or rotating at all...it is just gliding almost like a knuckleball...no movement other than the friction-less glide across the ground.

On it's vertical axis it has a MOI value of 4000 grams/cm^2. THIS is where I am confused. I understand this is the torque needed for a desired angular acceleration, but I need help.....If this object has no rotation on it's vertical axis b/c it is just gliding along the ground and some pressure of 4000 grams/cm^2 is placed on this object what does this do to the spinning/rotating along the vertical? Does 3999 grams/cm^2 not even change any motion?

I feel any pressure applied to this object would change the rotation so what does 4000 actual represent? Does it represent a certain predetermined amount of some units of rotation speed?

I hope I am articulating my confusion correct....I just don't know what the 4000 is actually telling me. I'm almost in my mind trying to predict what the stick of butter is going to do given a certain rock it hits on the ground that changes its motion assuming this rock applies 4000 of pressure or maybe other values of pressure.

thanks.

Doc Al
Mentor
On it's vertical axis it has a MOI value of 4000 grams/cm^2.
The correct dimensions for MOI would be mass*length2.

THIS is where I am confused. I understand this is the torque needed for a desired angular acceleration, but I need help.....
Think of MOI as the rotational analog to mass. Just as mass tells you, via Newton's 2nd law, how much force is required to produce a given translational acceleration, the moment of inertia tells you how much torque is required to produce a given rotational acceleration.

SteamKing
Staff Emeritus
Homework Helper
I have done some extensive self study on MOI but I don't understand it's meaning in application.

An example is imagine a stick of butter is dropped on the ground. Now ignoring friction and the other variables we can remove for learning purposes, let's assume the butter stick is kicked and it is gliding along the ground and it isn't rolling or rotating at all...it is just gliding almost like a knuckleball...no movement other than the friction-less glide across the ground.

On it's vertical axis it has a MOI value of 4000 grams/cm^2. THIS is where I am confused. I understand this is the torque needed for a desired angular acceleration, but I need help.....If this object has no rotation on it's vertical axis b/c it is just gliding along the ground and some pressure of 4000 grams/cm^2 is placed on this object what does this do to the spinning/rotating along the vertical? Does 3999 grams/cm^2 not even change any motion?

I feel any pressure applied to this object would change the rotation so what does 4000 actual represent? Does it represent a certain predetermined amount of some units of rotation speed?

I hope I am articulating my confusion correct....I just don't know what the 4000 is actually telling me. I'm almost in my mind trying to predict what the stick of butter is going to do given a certain rock it hits on the ground that changes its motion assuming this rock applies 4000 of pressure or maybe other values of pressure.

thanks.
Well, your first misconception about MOI is the units. MOI is measured in units of ML2, as in mass * length2, not mass / length2.
Pressure has units of F / A, or properly derived M*L*T-2*L-2 = M*L-1T-2.

In terms of the motion of a stick of butter (what is the vertical axis for this, anyway?) or a ball or a rock, the pressure due to contact is not what is essential to the analysis.

Thanks for the help and correction on units. How do you conceptualize what grams*cm^2 is. I can conceptualize mass b/c I can see a cubic cm of metal in my right hand, but I can't figure out what grams*cm^2 is.

My ignorant guess is 4000 grams*cm^2 is equivalent to the force of 4000 grams across and area of 1cmx1cm.

SteamKing
Staff Emeritus
Homework Helper
Thanks for the help and correction on units. How do you conceptualize what grams*cm^2 is. I can conceptualize mass b/c I can see a cubic cm of metal in my right hand, but I can't figure out what grams*cm^2 is.

My ignorant guess is 4000 grams*cm^2 is equivalent to the force of 4000 grams across and area of 1cmx1cm.

No, you're still stuck in thinking that the MOI is like some kind of pressure value.

The higher the value of the MOI of an object, the harder it is to rotate that object when a given amount of torque is applied. That's all it means.

For objects with most of their mass concentrated around the axis of rotation, their MOI will be lower than an object whose mass is distributed farther away from that same axis. That's why it's harder to twirl a dumbbell with two large masses connected by a bar than it is to twirl a single large mass with the same bar stuck thru it.

A.T.