Problem 1: Consider the yo-yo (of mass M and outer radius R) shown in the figure, where the string is being pulled with a force of magnitude F (F < Mg) at an angle θ to the horizontal. The radius of the inner axis is r (so that r < R). Assume that the angle θ ranges from 0 to π/2, and the coefficient of static friction with the ground is very large.
Part (a) In what direction will the yo-yo roll? Multiple Choice
1) To the left.
2) It cannot be determined; it depends on the angle θ.
3) It will stay motionless but spin.
4) It cannot be determined; it depends on the magnitude of force F.
5) To the right.
Part (b) Enter an expression for the critical angle (in radians, between 0 and π/2) at which the yo-yo will remain motionless. Use y = r/R to simplify your expression: Expression
Select from the variables below to write your expression: Note that all variables may not be required. acos(y), asin(y), atan(y), cos(θ), cos(φ), cos(0), sin(θ), sin(φ), sin(0), &, B, %, x, θ, d, g, h, m, n.
Part (c) Calculate this critical angle θe in degrees; if the yo-yo has an outer radius of 3.8 cm and an inner radius of 0.79 cm. Numeric A numeric value is expected and not an expression.