Take a 1kg point mass at the end of a 1 meter massless rod, free to rotate about a pivot at the other end of the rod. If I apply 1 unit of force to the point mass at a right angle to the rod, the point mass accelerates tangentially with 1 unit of acceleration and 1 unit of angular acceleration. However if I apply the same unit of force at 1/2 the length of the rod the point mass now accelerates at 1/2 a unit of acceleration and 1/2 a unit of angular acceleration. It’s the same force being applied but 1/2 of the momentum that force would usually supply is being lost somehow just by changing the location that it is being applied at. Where is that other 1/2 of the momentum going ?
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Since there is a hinge at the end of the ruler, linear momentum is never conserved because the hinge is applying force on the ruler when acted by a force. However, angular momentum is conserved about the hinge because. the torque due to the hinge is zero because it passes through it.
Piyush Lath
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In the second case you apply half the torque so the change in angular momentum is also halved. The moment of inertia is only a quarter so the change in angular speed is double. Its product with r is therefore the same as before halving r. Thus the tangential momentum is conserved.
Only the total linear momentum is conserved, which includes the system that the mass is connected to.
my2cts
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