Question

. Figure 1 shows a wheel (grey) with a central hub (green). It can roll freely on the flat, level tabletop. A beam (yellow) is pressed on the bottom of the hub and pulled to the right with force F. The radius of the large wheel is 13, the radius of the hub is 3. The beam, hub, and wheel all roll without slipping.

Which direction does the large wheel roll along the table?
How fast does it roll relative to the speed of the yellow beam?​

Answer 1

Answer:

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Answer 2

Answer:

As the wheel rolls a distance x, it rotates through angle x/R1 (in radians). For simplicity let us consider an angle of one radian. The beam moves in the same sense as the grey wheel and the green axle rolls through the same angle. So the beam moves R2 length with respect to the green axle. The beam therefore moves a distance R1-R2 = (13-3) = 10. The wheel rolls through a distance 13. So the wheel moves 13/10 = 1.3 times as far as the beam, in the direction the beam is pulled.