How Do You Calculate Torque with Tension and Gravity Forces?

[PhizKid]

Homework Statement

Just identify the torques on the bar by the Tension of the wire and the gravity on the bar, using the hinge as the axis of rotation, then find the horizontal and vertical components of the forces. For simplicity's sake, take theta to be 30 degrees.

Homework Equations

Torque = Ialpha
Torque = Force * radius * sin(angle)

The Attempt at a Solution

I found the radius for r_T, which is the radius of the torque of the Tension on the bar. But I don't know how to find the angles. Also, for the torque of the weight on the bar, there are 2 radii from the force of the weight to the bar (since the bar is part of the axis of rotation). I don't know which distance to use. The radius for the Tension was easy because it's direction in the center of the axis of rotation.

Then I don't know what the horizontal and vertical forces will be. It looks like Weight will be a vertical force, but I don't know what other components there are besides Tension and how to find the vertical and horizontal components of Tension.

 

[Bill Nye Tho]

$\tau$ = r x F

Ʃ $\tau$net = 0

(Counter-Clockwise being my positive reference frame)

The positive torque applied to the beam by the wire will be perpendicular component of Tension at a distance of L (length of the beam)

The negative torque applied to the beam by the weight of the beam will be the perpendicular component of weight at a distance of L/2.


F = ma

Ʃ Fnet = 0

You'll have the horizontal and vertical components of the tension & weight as well as the Fx & Fy forces at the hinge.

 

[PhizKid]

How do you know which direction the force of the hinge is pointing towards?

 

[haruspex]

How do you know which direction the force of the hinge is pointing towards?

If you are taking moments about the hinge, those forces have no ,moment so can be ignored.