Why why why? Sum of torque, changes in directions? This is

[riseofphoenix]

Why oh WHY do the arrows in this TORQUE problem keep alternating between SINE and COS

This is what they did:

I understand the whole Torque = F * r, but WHY (at the top of the diagram) is the arrow pointing up = (25 N)cos 30 and NOT sin and why is the arrow pointing to the right underneath it (25 N)sin 30 and not cos?? Same goes for the other arrows...I thought the x-axis (horizontal) was ALL COSINE and the y-axis (vertical) was SINE. This is so frustrating!
They keep doing this in ALL of their problems and it really confuses me.
They keep changing it from left to right...please help!

 

[PhizKid]

Forget the axes. Form triangles with the angles and determine the trig functions for the sides of the triangles you are looking for

 

[TSny]

Review the definition of torque. If you write torque as F*r (where r is the distance from the axis to the point of application of the force), then F is the component of the force that acts perpendicular to r. Thus, the formula should be $\tau$ = $F_{\bot}\:r$ where $F_{\bot}$ is the perpendicular component of the force.

[Edit: Ah, I think I misunderstood your difficulty. You are having trouble with finding the perpendicular component of the force. Follow PhizKid's advice! (You would use the cosine function for the x-component of a force only if the angle is measured from the x-axis.)]

 

[riseofphoenix]

Forget the axes. Form triangles with the angles and determine the trig functions for the sides of the triangles you are looking for

Ohhhh!
Ok.
Thanks!

 

[Nickie]

I can understand your frustration with this inconsistency in the use of sine and cosine in torque problems. However, it is important to remember that torque is a vector quantity and its direction is determined by the direction of the force and the direction of the lever arm (r). In the example you provided, the force is acting at an angle of 30 degrees from the horizontal, hence the use of sine and cosine in the calculation of torque. The horizontal component of the force (25 N * cos 30) creates a torque in the clockwise direction, while the vertical component of the force (25 N * sin 30) creates a torque in the counterclockwise direction.

In general, the use of sine and cosine in torque problems depends on the orientation of the force and the lever arm. If the force is acting parallel to the lever arm, only cosine will be used. If the force is acting perpendicular to the lever arm, only sine will be used. If the force is acting at an angle, both sine and cosine will be used to calculate the torque.

I understand that this may seem confusing at first, but with practice and understanding of the basic principles, you will be able to solve torque problems with ease. I recommend reviewing the concept of vector components and their relationship to sine and cosine to gain a better understanding of torque calculations.