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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 rimdesignated by the yellow-orange dot in the figure. (Intro 1 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 (Intro 2 figure) begin when the point is at the indicatedposition. One graph may be the correct answer to more than one part.

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The angular speed can be described as the ratio between the changes in angular displacement with respect to the time. The velocity of the angular axis is a vector value that is dependent on the magnitude of the change in is the direction that the displacement of the angular.

Concepts and ReasonThis question is based upon the concept of periodic motion.

Periodic motion refers to a motion which repeats itself after a set time period. These are distinguished by periodic functions such as [katex]\sin [/katex]

FundamentalsAngul velocity refers to the rate at which angular displacement changes.

[katex]\omega = \frac{{{\rm{Angular displacement}}}}{{{\rm{time}}}}[/katex]

The entire circular motion of an object is periodic if it moves at constant speed. After each complete rotation, the object returns to its original position. The object’s position along [katex]x{\rm{ }}[/katex]

(a)Coordinate system should be in the center of the wheel. The positive [katex]x{\rm{ }}[/katex]The graph [katex]F[/katex]

(b)The angular position at which a body stars with time is located is.[katex]\theta = \omega t[/katex]

Angular velocity [katex]\omega [/katex]

[katex]\theta \propto t[/katex]

The graph [katex]A[/katex]

(c)The motion along [katex]y[/katex]At [katex]t = 0[/katex]

After [katex]t = 0[/katex]

(d)Velocity [katex]v[/katex][katex]\omega = \frac{v}{r}[/katex]

The angle velocity is also constant. The wheel spins anticlockwise. The angular displacement, which is positive, increases at a constant rate according to the angular velocity. The graph should have a straight line and a positive slope. Because velocity is constant, angular velocity is also constant. Ans: Part A

The graph [katex]F[/katex]