Question #b10d6

1 Answer
Apr 2, 2017

See below


Newton's 2nd Law, #color(blue)( F = ma)# predicts that if the (net) force, #F#, on a body of mass #m# is zero, then that body's acceleration (which is denoted #a#) is zero.

ie: #F = 0 implies a = F/m = 0/m = 0#

So, if a body is not accelerating, it will experience no change in velocity. It will therefore remain at rest - or continue to move at a constant velocity.

Newton's 1st Law states, roughly, that an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

So his 1st law looks to be a "mere" sub-set of his 2nd.

Seems odd but it may have been done this way to confront, head-on, Aristotle's idea that everything that is in motion is thus because there is some cause (ie a force) that is driving that motion. Who knows? Newton was hardly a team-player :)

Other thing worth stressing, I think, is that the 2nd Law has many manifestations. We start at:

#F = ma#

But it's really about the net force on an object, so:

#sum F = ma#

And these are vectors , ie direction matters. A particle moving at constant speed but changing direction is accelerating. Eg uniform circular motion. So:

#sum vec F = m vec a#

Interim calculus step:

#sum vec F = m (d vec v)/dt#

Really important where mass is not constant:

#sum vec F = (d (m vec v))/dt#

Consolidating all of the above:

#sum vec F = (d vec p)/dt#

The third law is IMHO the truly interesting insight - it leads to universal conservation of momentum.