Understanding free-body diagram: Circular Hoop

[efn]

Homework Statement

Understanding the free-body diagram of a bead on a circular hoop. I am calculating all forces on with x and y direction and a little confused.

• Why is sin*angle_x and cos*angle_y reverted in this? Usually i go sin with y and x with cos.
• Why is the force n=mg/(cos*beta) and not n=mg-(cos*beta)

See the attempted solution and help understanding this. Thanks.

Homework Equations

Newton's Law

The Attempt at a Solution

 

[Isaac0427]

What is the direction (maybe this is different terminology than you are used to, but direction is measured from due east counterclockwise) of the vector N? Hint: it is not β. What is β? Do you know how to switch from sine to cosine? Let's see if you can figure it out from there.

 

[efn]

What is the direction (maybe this is different terminology than you are used to, but direction is measured from due east counterclockwise) of the vector N? Hint: it is not β. What is β? Do you know how to switch from sine to cosine? Let's see if you can figure it out from there.

Hey, i understand it this way. The circular direction is in x direction: a_rad. β is the angle. If you say direction is measured from due east counterclockwise of the vector N. Still not sure how to position the bead.

 

[Isaac0427]

Hey, i understand it this way. The circular direction is in x direction: a_rad. β is the angle. If you say direction is measured from due east counterclockwise of the vector N. Still not sure how to position the bead.

So β is the heading of N. Heading is measured from due north clockwise. Think about the direction of N, measured from due east counterclockwise. What I am trying to get at, is that when you use direction, x is cosine and y is sine, but when you use heading, y is cosine and x is sine. There are two ways to understand this; geometrically and numerically. First, for the numerical method, see if you can come up with a relationship between heading and direction.

 

[efn]

So β is the heading of N. Heading is measured from due north clockwise. Think about the direction of N, measured from due east counterclockwise. What I am trying to get at, is that when you use direction, x is cosine and y is sine, but when you use heading, y is cosine and x is sine. There are two ways to understand this; geometrically and numerically. First, for the numerical method, see if you can come up with a relationship between heading and direction.

So, i tried to draw it this way. Alternative we could put the sine line at the end and get positve direction. Hopefully this is the right way of thinking.

 

[Isaac0427]

So, i tried to draw it this way. Alternative we could put the sine line at the end and get positve direction. Hopefully this is the right way of thinking.
View attachment 197533

I'm not quite sure what you're doing there. Go back to the original drawing and try to find the direction. It is the angle that N makes with the x-axis measured counterclockwise.

 

[efn]

I'm not quite sure what you're doing there. Go back to the original drawing and try to find the direction. It is the angle that N makes with the x-axis measured counterclockwise.

So, far this is what i get from original drawings.

Next thing revert this into positive directions?

 

[Isaac0427]

So, far this is what i get from original drawings.

View attachment 197579

Next thing revert this into positive directions?

Those are not the original drawing. Why don't you take my first suggestion on finding the relationship between heading and direction. Your question is about why sine is used for the x component instead of the y, right?

 

[efn]

Those are not the original drawing. Why don't you take my first suggestion on finding the relationship between heading and direction. Your question is about why sine is used for the x component instead of the y, right?

The drawing i provided now are the original exercise drawings. The one in the first post is the free-body diagram solution for that exercise.

Yes, i still wondering why sine is used for x component. But i am still struggling to understand this. B_angle is the Heading of N from its right side, B_angle is also the bottom from its left side. How do you want me to get this?

 

[haruspex]

i still wondering why sine is used for x component.

The diagram is confusing. It seems to mark both the angle to the vertical and the angle to the horizontal as β. To be consistent with the equations, it must be the angle to the vertical. Ignore the β just left of the vertical dashed line.
Does that resolve it for you?