# Which system to apply conservation of momentum to?

• chris25
In summary, the question is whether conservation of angular momentum should be applied to the person, the swing, or the person-swing system. The angular momentum of the person-swing system is conserved, but the individual angular momentums of the person and the swing are not. The necessary torque for the person-swing system to maintain angular momentum comes from the force of static friction between the swing and the person's feet.

#### chris25

Homework Statement
A person stands on the seat of a swing and squats down, so that the distance between their center of mass (CM) and the swing’s pivot is L0. As the swing gets to the lowest point, the speed of their CM is V. At this moment, they quickly stand up, and thus decrease the distance from their CM to the swing’s pivot to L'. Immediately after they finish standing up, their CM speed is v0.
Relevant Equations
Comes from F=ma 2020b
Conservation of Angular Momentum
For this problem I was very confused whether conservation of angular momentum should be applied to the person, the swing or the person-swing system. It seems to me that there is no net torque on any of the three systems I listed above. However, it seems that the angular momentums of the three separates systems I listed cannot all be conserved simultaneously. Which system should I use, and for the systems wthere angular momentum is not conserved, where does the net torque come from? Thanks

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If you take as your system the person + the swing, then the angular momentum of this system is conserved. As the person stands up, his/her/zes CM at its new radius must acquire a smaller angular velocity for the system's two components to continue moving as one. The torque that provides the needed angular acceleration opposite to the angular velocity comes from the force of static friction exerted by the swing on the person's soles. Of course an equal and opposite torque is exerted by the soles on the swing and the net torque on the two-component system is zero.

chris25 and Lnewqban
kuruman said:
The torque that provides the needed angular acceleration opposite to the angular velocity comes from the force of static friction exerted by the swing on the person's soles
Not the soles, I think. Unless holding on to the ropes either side, the swinger would be thrown forwards off the seat.