4.14 by Paul is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

# 4.14

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4.14 by Paul is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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I may be wrong but shouldn't the angular velocity be +.296 rad/s?

Isn't k x -i = +j?

And isn't that the same with the angular acceleration as well?

I think result given is correct.

In case you need to brush up on cross products.

sorry I was using my left hand... its late...

Thanks!

Shouldn't the direction of the angular acceleration of drum A be counter clockwise (+k)? Why do you have it labelled -k

In the tenth edition the problem says: "For the instant presented, drum has counterclockwise angular velocity of 6 rad/s that is

decreasingby 4.5 rad/s^2". That the CCW angular velocity is decreasing tells me that the acceleration is clock-wise.Is this problem written differently in the eleventh edition?

I have the 11th edition, and your quoted statement starting with "For the instant presented," is the exact sentience shown on problem 4.14 in the 11th edition.

No it is written correctly, I understand now. Thanks

This is the exact same problem from the 11th edition

How do you know the point O does not accelerate in the i direction, and point A and C do? Is it because point O is at the center of angular acceleration? If so, how do we know O is at the center?

Right you are, doesn't have any centripetal acceleration because it is the center of rotation. As to your second question, we can only tell that is the center by our intuitions about the motion of the system. Since the cables seem to be lowering the central body straight down (indeed the problem confirms this "...is lowered by the two pulleys...") we can take its translation as downward. This implies that point has a straight trajectory in the direction. The other points will have a sinusoidal trajectory through space as they undergo translation and rotation.