Word for word, from the problem:
"A person’s center of mass is easily found by having the person lie on a reaction board. A horizontal 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 60 kg woman lies on the reaction board with her feet over the pivot. The scale reads 25 kg. What is the distance from the woman’s feet to her center of mass?"
T=Iα (torque = moment of inertia times angular acceleration)
T=rFsin∅ (torque = radius times the force times sine of the angle between the radius and the force)
T=rFt (torque = radius times component of force perpendicular to the moment arm)
l=rmvsin∅ (angular momentum = radius times mass times velocity times the sine of the angle between the radius and the force)
The Attempt at a Solution
So the scale reads 25kg, and I thought maybe that force could be found using F = ma. So I did that and got a force of 245N. I figure that force is perpendicular to the moment arm, so I multiplied it by 2.5m and got a torque of 612.5N⋅m. From there I'm kind of stuck though. I think it maybe also has something to do with angular momentum?