Angular Acceleration: Clarifying What αz is?

[oliampian]

Homework Statement

This is not really a question on how to solve the problem, I'm just trying to get clarification on something. For angular acceleration, α, can someone explain to me what α_z is? And why does α_z = α / R = α_y? I understand the rest of the problem, I just don't understand where or what α_z is and how α_z = α / R = α_y. Thanks in advance for any help given!

 

[TSny]

For angular acceleration, α, can someone explain to me what α_z is?

$\alpha_z$ apparently represents the angular acceleration for rotation about the z-axis.

And why does α_z = α / R = α_y?

The print in the picture is small and hard to read. In equation (2) I think it states that $\alpha_z = \large \frac{a}{R}$, not $\alpha_z = \large \frac{\alpha}{R}.$

 

[oliampian]

$\alpha_z$ apparently represents the angular acceleration for rotation about the z-axis.

The print in the picture is small and hard to read. In equation (2) I think it states that $\alpha_z = \large \frac{a}{R}$, not $\alpha_z = \large \frac{\alpha}{R}.$

Ohhh, you're right about the a/R not α/R. But can you explain to me why does a/R = a_y?

 

[TSny]

Ohhh, you're right about the a/R not α/R. But can you explain to me why does a/R = a_y?

They aren't claiming that a/R = a_y.

The R cancels: (1/2)MR(a/R) = (1/2)Ma_y. The "a" on the left is the same as a_y.

 

[oliampian]

They aren't claiming that a/R = a_y.

The R cancels: (1/2)MR(a/R) = (1/2)Ma_y. The "a" on the left is the same as a_y.

Ok I see. And just to clarify, if I divide a linear acceleration by the radius R then we get angular acceleration?

Nvm! Figured it out. Thank yoooou! :)