Rotation - constant properties when met force is 0

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cupid.callin
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Homework Statement


this was a question in my book ...

If the resultant force (external) acting on a body is 0, then from an inertial, one can surely say that

(A) Linear momentum does not change with time
(B) kinetic Energy does not change with time
(C) Angular momentum does not change with time
(D) Potential Energy does not change with time

The Attempt at a Solution



I know that (A) is correct and (C) (D) are wrong

i want to talk about (B)

According to energy conservation principle ...

If no external force acts and all the internal forces are conservative ... mechanical energy remains conserved (or constant ... please correct me ... but i guess conserved)

and like potential energy is changing so kinetic should also ...

But K = 0.5 mv2
so dK/dt = mv (dv/dt) = mva

of a =0 so K is constant ...

So what is really right?
 

Discussion

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why?

A is right of course
C is wrong as net 0 force can still have some torque and thus angular acceleration
D is wrong as suppose a body is coming down in a light with constant velocity v

net force of mg and normal rxn is 0 so acceleration is 0

but pot. energy dec

but also in this case v and thus kinetic energy is constant
 
If the potential energy is changing, obviously the corresponding field is exerting a force.
However, if the resulting force is zero, there must be another unspecified force opposing this.
The net result would be that the potential energy changes, but the kinetic energy is constant.
Note that this means that the total energy increases.

Btw, C is open for discussion.
You might say that the angular momentum in this case would be infinite, since there would be no acting radial force. Does it change?
 
Last edited:
The OP is correct about C. Consider a pure couple: Two forces acting on an object such that the vector sum of the two forces is zero but with the two forces applied at different points on the object. The net force is zero, but the net torque is not.

The OP is also correct about D. The OP's answer would have been wrong if both forces were known to be conservative forces. However, there is nothing in the problem statement that says that the two forces are both conservative. To the OP: Your perceived problem with statement B is that you are assuming mechanical energy is conserved, and that is only true in the case of conservative forces.