You are an enterprising physics student who has just been asked to solve Norton’s dome, a thought experiment about a ball rolling down a hill. For 10 points each:
[10e] You begin by computing the tangential gravitational force on a point mass sliding off the dome so that you can plug it into this law, which states that the force on an object is equal to the rate of change of momentum.
ANSWER: Newton’s second law [prompt on F equals m a]
[10m] To your surprise, you discover that solutions to Newton’s second law exist but lack this corresponding property, thus apparently providing an example of indeterminism in physics.
ANSWER: uniqueness
[10h] You realize that the dome’s non-determinacy may be sidestepped by observing that at time zero, net force is undefined. Requiring the ball to remain on the dome may thus be modeled as this kind of constraint, in which some function of the generalized coordinates and time is set equal to zero.
ANSWER: holonomic constraints
<JC, Physics>