Question

A man walking on a tightrope carries a long a pole which has heavy items attached to the two ends. If he were to walk the tight-rope with just a pole, what difference would it make to his balance? Discuss this in terms of angular rotation, angular momentum, and moment of inertia.

Answer 1

Answer:

 I_weight = M L²

this value is much larger and with it it is easier to restore balance.I

Explanation:

When man walks a tightrope, he carries a linear velocity, this velocity is related to the angular velocity by

            v = w r

For man to maintain equilibrium needs the total moment to be zero

             ∑τ = I α

              S  τ = 0

The forces on the home are the weight of the masses, the weight of the man and the support on the rope, the latter two are zero taque the distance to the center of rotation is zero.

Therefore the moment of the masses and the open is the one that must be zero.

If the man carries only the bar, we could approximate it by two open one on each side of the axis of rotation formed by the free of the rope

              I = ⅓ m L² / 4

As the length of half the length of the bar and the mass of the bar is small, this moment is small, therefore at the moment if there is some imbalance it is difficult to recover.

If, in addition to the opening, each of them carries a specific weight, the moment of inertia of this weight is

             I_weight = M L²

this value is much larger and with it it is easier to restore balance.