## 11 thoughts on “4.14”

1. Andre Tayar says:

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

Isn't k x -i = +j?

1. Andre Tayar says:

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

2. tutorpaul says:

I think result given is correct.

1. Andre Tayar says:

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

Thanks!

2. seguntytler says:

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

1. tutorpaul says:

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

1. blake.wallace95 says:

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.

2. seguntytler says:

No it is written correctly, I understand now. Thanks

3. blake.wallace95 says:

This is the exact same problem from the 11th edition

4. beaujakob says:

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?

1. tutorpaul says:

Right you are, $O$ doesn't have any centripetal acceleration because it is the center of rotation. As to your second question, we can only tell that $O$ 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 $O$ has a straight trajectory in the $-\hat j$ direction. The other points will have a sinusoidal trajectory through space as they undergo translation and rotation.