A particle is to move in xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle if the magnitude of its angular momentum about the origin is (a) 4.0 kg·m2 /s, (b) 4.0t2 kg·m2 /s, and (c) 4.0/t2 kg ·m2 /s? answer in steps wise..
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Explanation:
We use a right handed coordinates system with
k
^
directed out of the xy plane so as to be consistent with counterclockwise rotation (and the right hand rule). Thus all the angle momenta being considered are along the −
k
^
direction;
l
=−4.0t
2
k
^
in SI units.
Taking the derivative with respect to time, we obtain the torque:
τ
=
dt
d
l
=(−4.0
k
^
)
dt
dt
2
=(−8.0 t N.m)
k
^
This vector points in the −
k
^
direction (causing the clockwise motion to speed up) for all t>0
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