Question

While placing a compact disc into a CD player, you notice a small chip on it\'s edge. But you attempt to play the CD anyway by placing the CD into the player\'s deck with the chip at θ0 = 10.0° as measured from the x axis. The CD begins to rotate with angular acceleration α = 2.49 rad/s2. If the CD has been spinning for t = 3.51 s and the disc has a radius of r = 6.00 cm, what are the x–y coordinates of the chip after this time, assuming the center of the disc is located at (0.00,0.00).
According to my calculations it should be x = -2 and y = 5.8 but those were incorrect.

Answer 1

Answer:

  (x, y) ≈ (-5.89, 1.16)

Step-by-step explanation:

We assume the CD is still accelerating at the same rate at the end of the given time period. The angular position will be found from ...

  θ(t) = θ₀ + (1/2)a·t²

Filling in the numbers given, we get

  θ(3.51) = (10π/180) + (1/2)(2.49)(3.51²) = 15.51306 . . . radians

The x-y coordinates will be found from ...

  (x, y) = radius·(cos(θ), sin(θ)) ≈ 6·(-0.981066, 0.193674)

  (x, y) ≈ (-5.89, 1.16)

_____

For the trig functions, the calculator must be in radians mode, unless you have converted the angles to degrees.