Be careful of +/- signs!

String massless=along the string tension is the same

If tension r same, want to pull in diff rotate by same amount, Tnet=0 and rotate=0

So only rotate if there's a net T, which can only b if string yank on pulley only bc of friction!

No slipping, f=fs

Bc pulley has the mass, now tension on 2 side r diff

Tension is only same when: string/pulley massless, and no friction

Bc of friction, pulley and string have same vtan since no slip and move together, motion of string and pulley 2gether

On circumference of pulley

𝛼=atan pulley/R=astring/R=a/R

Use coord sys positive x and y

Coord sys lock that CCW is + if R and up is + bc must go from +x to +y axis, but also can use diff coord sys for each sys

Solving

Use second law (both form) for the 2 masses and pulleys (sum T=I 𝛼

3 unknown: T1, T2 , a

3 equations, plug in 2 to 1 to find the acceleration a

Torque is j Frcmsin(90)=Tension • r since the radius to edge is exactly the pt where the F start

Remember to solve for the inertia of the thing. But in T=I 𝛼, rewrite as sum torque (b careful of dir of rotation and T=Frperp)= +/- I 𝛼 (depend on dir)

Then after get a, 𝛼pulley=a/R and thats it! 10th EditionDavid Halliday, Jearl Walker, Robert Resnick7,188 solutions

10th EditionJulio de Paula, Peter Atkins1,315 solutions

3rd EditionMary L. Boas3,355 solutions

4th EditionRandall D. Knight3,508 solutions