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
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
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 Resnick
10th EditionJulio de Paula, Peter Atkins
3rd EditionMary L. Boas
4th EditionRandall D. Knight