A certain drawbridge can be modeled as a uniform 1.6•10^4 N bar, 11.0 m long, pi

Question

A certain drawbridge can be modeled as a uniform 1.6•10^4 N bar, 11.0 m long, pivoted about its lower end. When this bridge is raised to an angle of 60 degrees above the horizontal, the cable holding it suddenly breaks, allowing the bridge to fall. At the instant after the cable breaks. A) at the instant after the cable breaks what is the torque on this bridge about the pivot? B) at the instant after the cable breaks at what rate is its angular momentum changing? A certain drawbridge can be modeled as a uniform 1.6•10^4 N bar, 11.0 m long, pivoted about its lower end. When this bridge is raised to an angle of 60 degrees above the horizontal, the cable holding it suddenly breaks, allowing the bridge to fall. At the instant after the cable breaks. A) at the instant after the cable breaks what is the torque on this bridge about the pivot? B) at the instant after the cable breaks at what rate is its angular momentum changing? A) at the instant after the cable breaks what is the torque on this bridge about the pivot? B) at the instant after the cable breaks at what rate is its angular momentum changing?

Explanation / Answer

Torque is due to weight of the bridge, acting at it's center.
Vertical line of force of weight is L cos 60 /2 from the pivot.

Torque on the bridge is line of force x perpendicula distance of line of florce from pivot
Torque = W L cos 60 /2
          = 1.6x104 * 11 * 1/2 * 1/2 = 4.4 x104 Nm

2) Rate of change of angular momentum = torque = 4.4x104 Nm

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