1. The problem statement, all variables and given/known data A hoop sits on a bus. The bus begins to accelerate toward the right with acceleration a1, shown below. The bus tires do not slip on the road. As the bus accelerates, the hoop begins to roll without slipping on the rigid floor of the bus and has rightward center of mass acceleration a2. 1) The bus wheel's radius is r1. Its center of mass velocity and acceleration are v1 and a1; the bus wheel's angular velocity and angular acceleration around its center of mass are ω1 and α1. 2) The hoop's radius is r2. Its center of mass velocity and acceleration are v2 and a2; the hoop's angular velocity and angular acceleration around its center of mass are ω2 and α2. Point P on the wheel is in contact with the rigid bus floor. Which equations are implied by each of the constraining conditions indicated in the figure? The sixth equation that was cut out accidentally is v1 = ω1r1 3. The attempt at a solution My initial thoughts: Intuitively, I imagine that the hoop will roll and accelerate to the back of the bus. I do not imagine that it must roll at a constant velocity relative to the bus. No where in the problem is it implied that μstatic's are equal, and we could be at the point where the hoop or wheel is about to slip. Condition X Implies: a2 = α2r2 But... is this incorrect because the floor moves? aP = a2 If the hoop doesn't slip, then the center of mass should be vertically aligned with the center of mass at all times. Condition X Eliminates: vP = v1 AND v2 = ω1r1 (for t ≠ 0s) aP = a1 If the hoop rolls w/o slipping, and vP = v2, then there must be a non-zero relative velocity between the CoM of the hoop and the bus. Since both start at rest, their linear accelerations cannot be equal. Condition Y Implies: v1 = ω1r1 Can anyone help? Thanks much!