Issue with angles in torque problem?

In summary, the solution listed the angle for b) as sin(115°) and for c) as sin(160°). I'm confused on where the 115° and 160° came from when the picture showed the angles as 25° and 70° respectively. Am I missing something? Thanks!
  • #1
fightboy
25
0
Ok so for this example you have to calculate the net torque about an axis that passes through the hinges in each of the following cases in the image:
chapter 8 physics problem.jpg


a) and c) were fairly straightforward to calculate but i had issues with b) and c). The solution listed the angle for b) as sin(115°) and for c) as sin(160°). I'm confused on where the 115° and 160° came from when the picture showed the angles as 25° and 70° respectively. Am I missing something? Thanks!
 
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  • #2
fightboy said:
Ok so for this example you have to calculate the net torque about an axis that passes through the hinges in each of the following cases in the image:
View attachment 73087

a) and c) were fairly straightforward to calculate but i had issues with b) and c). The solution listed the angle for b) as sin(115°) and for c) as sin(160°). I'm confused on where the 115° and 160° came from when the picture showed the angles as 25° and 70° respectively. Am I missing something? Thanks!

There's a small typo in your text above. I believe you mean that a) and d) are easy, and b) and c) are confusing you. :smile:

It is indeed a bit strange to use sin() to calculate the torque and show those angles, but it can be done of course. It's much more normal to use the cos() function, given the angles listed in the diagrams. Are you familar with the dot product?

Also, are you familiar with using the vector cross product to calculate the vector torque (it has magnitude and direction)? If you haven't gotten there yet, don't worry about it for now. If you have seen it, then you know that the sin() is used in it, but for the complementary angle to the one shown in your problem's diagrams.

Does that make sense?
 
  • #3
All four look equally easy to me as log as you keep in mind that it only the force perpendicular to the arm that is relevant. If the given force makes angle [itex]\theta[/itex] with the vertical, then the component that is perpendicular to the arm is [itex]F cos(\theta)[/itex].
 
  • #4
Oh, I think you must post the entire problem not just the diagram.
 

1. What is torque and how does it relate to angles?

Torque is a measure of the rotational force that is applied to an object. It is calculated by multiplying the force applied to an object by the perpendicular distance between the point of force and the axis of rotation. Angles are important in torque because they determine the direction of the force and can impact the resulting torque value.

2. What is the difference between positive and negative angles in torque?

In torque problems, positive angles typically refer to a counterclockwise rotation while negative angles refer to a clockwise rotation. The direction of rotation can affect the direction and magnitude of the resulting torque.

3. How do I determine the angle in a torque problem?

The angle in a torque problem can be determined by using a protractor or measuring tool. It is important to ensure that the angle is measured from the correct point of reference and in the correct direction to accurately calculate torque.

4. Why is the angle important in calculating torque?

The angle is important in calculating torque because it determines the direction of the force and can impact the resulting magnitude of the torque. A small change in angle can result in a significant difference in the torque value.

5. What is the unit of measurement for torque and how is it calculated?

The unit of measurement for torque is typically Newton-meters (Nm) in the metric system and foot-pounds (ft-lb) in the imperial system. To calculate torque, you multiply the force applied to an object by the perpendicular distance from the point of force to the axis of rotation.

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