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lets consider rotation in the xy plane so that L points in the direction of the z axis.

the angular momentum is defined as L=rxp where r is the position vector and p the linear momentum.

suppose that p is constant in magnitude and perpendicular to r so that we have a constant rotation with constant angular velocity.

my problem is now that when one makes r=2r (makes r twice as large) then for the angular momentum to stay constant the linear momentum needs to drop by a factor of 2.

now one can also write L=rmv for the rotation described above now the problem comes with the torque T=rma witch means that if T is supposed to stay constant when r=2r then a=a/2

but this would mean that the force has dropped just because r did rise.

now im wondering what kind of physical meaning this would have, and i know that it must have some because of the lever.

now before i bite my thong explaining things, could someone please point to my mistakes thx