Posted by rosa on Wednesday, November 13, 2013 at 10:59am.
A yoyo of mass m rests on the floor (the static friction coefficient with the floor is mu ). The inner (shaded) portion of the yoyo has a radius R1 , the two outer disks have radii R2 . A string is wrapped around the inner part. Someone pulls on the string at an angle Beta (see sketch). The "pull" is very gentle, and is carefully increased until the yoyo starts to roll without slipping.
For what angles of beta will the yoyo roll to the left and for what angles to the right?
a) YoYo rolls to the left if sin beta<R1/R_2 , and to the right if sin beta> R_1/R_2.
b)YoYo rolls to the left if sin beta>R1/R_2 , and to the right if sin beta<R_1/R_2
c)yo yo rolls to the left if cos beta< R_1/R_2 and to the right if cos beta>R_1/R2
d)yo yo rolls to the left if cosbeta>R_1/R_2 and to the right if cosbeta< R_1/R_2 .

Do not understand  Damon, Wednesday, November 13, 2013 at 12:02pm
The reason I am not answering is that without a drawing I find the question incomprehensible.

Physics Important please  rosa, Wednesday, November 13, 2013 at 1:42pm
Hi Damon,
R_1 is inner radius and R_2 is outer radius of yo yo which looks like concentric circle and beta is the angle in right side of that yo yo. I hope this will help to complete the question. I don't know how to draw image here. 
Physics Important please  rosa, Wednesday, November 13, 2013 at 2:24pm
Hi, Damon I got it. Thank you