Graphing rotation & linear quantites

In summary, rotation and linear quantities are two types of motion that can be described using graphs. The main difference between them is the type of movement they represent, with rotation being circular and linear quantities being straight-line. To graph them, data points are plotted on a graph with the independent variable on the x-axis and the dependent variable on the y-axis, forming a circular pattern for rotation and a straight line for linear quantities. Common units of measurement for rotation include degrees, radians, and revolutions, while for linear quantities, they include meters, kilometers, feet, and miles. The slope of the graph can be used to determine the speed of rotation or linear motion, with steeper slopes indicating faster motion. Additionally, a graph of rotation or linear
  • #1
thinktank75
19
0
While working on her bike, Amanita turns it upside down and gives the front wheel a counterclockwise spin. It spins at approximately constant speed for a few seconds. During this portion of the motion, she records the x and y positions and velocities, as well as the angular position and angular velocity, for the point on the rim designated by the yellow-orange dot in the figure. View Figure Let the origin of the coordinate system be at the center of the wheel, the positive x direction to the right, the positive y position up, and the positive angular position counterclockwise. The graphs View Figure begin when the point is at the indicated position.
http://img274.imageshack.us/img274/3427/1011381be.jpg

Which of the graphs corresponds to x position versus time?
-> would this be a [ C ] because the position doesn't move as time passes by? Or is this different for rotational?

Which of the graphs corresponds to angular position versus time?
Would this be [ E ] since it starts with position 0, then it goes to a positive position, then negatice, to posive etc?

Which of the graphs corresponds to y velocity versus time?
What do they mean by y velocity? (verticle velocity)
would the verticle velocity do negative to positive and back to negative again? Is this possible? so graph [ G ] ?

Which of the following graphs corresponds to angular velocity versus time?
I have no idea...

Thanks :approve:
 
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  • #2
The velocity vector is tangent to the circle, and you can decompose it to x and y components, so I guess that's what was meant ba x and y velocity.
 
  • #3
radou said:
The velocity vector is tangent to the circle, and you can decompose it to x and y components, so I guess that's what was meant ba x and y velocity.

What about the other responses? I'm not too 100% sure... would there be a point when velocty y would be 0? so it must be one of the sin or cos graphcs?
 
  • #4
thinktank75 said:
What about the other responses? I'm not too 100% sure... would there be a point when velocty y would be 0? so it must be one of the sin or cos graphcs?

Think about it this way: fix your eyes on a point on the rotating circle. The velocity vector will always be tangential to the circle, so, at which point will the y-component of velocity vanish? (Hint: the two points at which there is only the x-component.)
 
  • #5
Would it be [ E ]? the velocity can have a negative value? (since Y is negative) but why isn't it a straight line? isn't the velocity constant?

Edit: E was wrong, but the wheel starts rotating at position 15 minutes on a clock.. if you can visualize that :)
 
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  • #6
Which of the graphs corresponds to angular position versus time?

Okay, angular position is given (for constant angular velocity, as stated) , by [tex]\phi(t)=\omega\cdot t[/tex], where [tex]\omega[/tex] is angular velocity, so it's a linear function.

Which of the following graphs corresponds to angular velocity versus time?

Well, we said that angular velocity is constant, right? :smile:
 
  • #7
radou said:
Which of the graphs corresponds to angular position versus time?

Okay, angular position is given (for constant angular velocity, as stated) , by [tex]\phi(t)=\omega\cdot t[/tex], where [tex]\omega[/tex] is angular velocity, so it's a linear function.

Which of the following graphs corresponds to angular velocity versus time?

Well, we said that angular velocity is constant, right? :smile:


Since they're linear ('cause they're constant) is it the graph C? (positive, but what about the linear graphics that is negative, decreasing and increasing, those are confusing me)
 
  • #8
thinktank75 said:
Since they're linear ('cause they're constant) is it the graph C? (positive, but what about the linear graphics that is negative, decreasing and increasing, those are confusing me)

Well, that depends if you defined counter clockwise (I think you said that was the direction of rotation) as positive or negative.
 
  • #9
radou said:
Well, that depends if you defined counter clockwise (I think you said that was the direction of rotation) as positive or negative.

since its counterclockwise it would go to positive (so increasing) but then in reaches right back down to negative.. so non of the line graphics work?
 
  • #10
thinktank75 said:
since its counterclockwise it would go to positive (so increasing) but then in reaches right back down to negative.. so non of the line graphics work?

It does not reach anything negative. Angular speed is constant. If you accepted counter clockwise as positive, then it's the graph on the positive side.
 

FAQ: Graphing rotation & linear quantites

1. What is the difference between rotation and linear quantities?

Rotation and linear quantities are types of motion that can be described using graphs. The main difference between them is the type of movement they represent. Rotation refers to circular or rotational motion, while linear quantities refer to straight-line motion.

2. How do you graph rotation and linear quantities?

To graph rotation and linear quantities, you will need to plot the data points on a graph with the independent variable on the x-axis and the dependent variable on the y-axis. For rotation, the data points will form a circular pattern, while for linear quantities, the data points will form a straight line.

3. What are some common units of measurement for rotation and linear quantities?

For rotation, common units of measurement include degrees, radians, and revolutions. For linear quantities, common units of measurement include meters, kilometers, feet, and miles. The specific units of measurement used will depend on the type of rotation or linear quantity being measured.

4. How can you use a graph to determine the speed of rotation or linear motion?

The slope of a graph representing rotation or linear motion can be used to determine the speed of the motion. For rotation, the slope will be equal to the angular velocity, while for linear motion, the slope will be equal to the velocity. The steeper the slope, the faster the motion.

5. What other information can be obtained from a graph of rotation or linear quantities?

In addition to speed, a graph of rotation or linear quantities can also provide information about the direction of motion, acceleration, and displacement. The shape of the graph can also indicate if the motion is constant or changing over time.

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