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Lost1ne

- 47

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## Homework Statement

(Problems/diagrams referenced are attached as images.)

## Homework Equations

Net torque about an origin = time derivative of the angular momentum vector about the same origin.

## The Attempt at a Solution

I've solved these problems before, but I'm now looking back at them and questioning my understanding of them.

I've noticed how many problems are illustrated with what seems to be a cross-section of the object that we are analyzing in that we draw the problem such that our origin (that we self-select for calculating angular momentum and torque) and the center of mass of our object are in the same plane.

It seems that the reason for this is to make the problem simpler to solve, but is it always an accurate method to use? Should I view this as an assumption made to make the problem simpler to solve, particularly in the car problem where clearly a 3D vector would have to be used to illustrate the vector from the center of mass to the bottom of the tire where static friction is applied. (Solving this problem in a 2-D world allows you to use "2 feet", given in the problem, as the perpendicular component of this vector, making the torque calculation about the center of mass simpler. However, in 3-D, it seems that this perpendicular vector would be composed of two sub-components, one to get from the center of mass straight to the ground, and another to get from there to the same line where the static friction vector would be found on.)

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As it relates to the pulley image, can we agree that choosing our origin to be in a different plane would most certainly change our calculations? Is my way of thinking correct?: In this scenario, not only is the origin simply in the same plane as the pulley center of mass, but the origin is chosen as the center of mass. This eliminates the need to worry about an orbital angular momentum component which makes this problem (or similar problems where this approach is taken) easier to solve. Drawing and solving our problem in this 2-D manner is then encouraged.

If we chose our origin to be on this axis of rotation but

*not*on the center of mass or not on this axis of rotation at all, we would get a more complex 3-D or 2-D (if the origin is still in the same plane as the center of mass) where we would then have to be concerned with an angular momentum component. (Although, however, in this specific pulley scenario, it seems that the orbital component will still be zero as the center of mass velocity of the pulley is constrained to be zero.)

Edit: The car problem also uses the origin as the center of mass as we elect to sum the torques about the center of mass. I guess I would like to know why we treat the center of mass as if it is in the same plane as the static friction and normal forces. Am I missing something conceptually here, or is this merely an assumption made to simplify the problem?

#### Attachments

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