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s G Google YouTube s Dental! App S MY TSU wEB Blackboard Learn t DST Home | GradesFirst P Pandora Radio - List | Off A small sphere rotates counterclockwise in a circle of radius 3.5 m Light source (parallel) with a constant angular Angular speed of 8.00 rad/s, as shown in the Active Figure. At 0, the particle has an x coordinate of 1.3 m and is moving to the right. A source of parallel rays of light above the sphere produces a shadow on the table, as shown in the Active speed .0 rad/s 8.0 6.5 -6.0 -5.5 5.0 3.5 3.0 2.0 gure -0.5 (A) Determine the.x coordinate as a function of time (B) Find the x components of the particle's velocity and acceleration at any time t. start reset Display in a New Windovw Conceptualize The location of the shadow is found by imagining a vertical line from the center of the sphere to a point on the screen. As the sphere rotates around in a circle at constant angular speed, the point on the screen moves back and forth Categorize The problem examines the relation between simple harmonic motion and the time dependence of the x coordinate of a particle in circular motion Analyze (A) Determine the x coordinate as a function of time. The position of the center of the sphere can be described by the polar coordinates r and , where r is the distance from the center of the sphere to the center of the circular path and is the angle the radius makes with the positive x axis. Since changes at a constant rate, it satisfies:

Explanation / Answer

The solution whihc is given is correct.

here are the final answers.

a) x = 3.5*cos(8.00*t - 0.021)

b)

vx = 28*sin(8.00*t - 0.021)

ay = -224*cos(8.00*t - 0.021)

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