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 = 15.2° as measured from the x axis. The CD begins to rotate with angular acceleration α = 2.31 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).

Answer 1

θ0 = 15.2°=(15.2*2*3.14/360)rad

θ0 =0.265 rad

t =3.51s, r = 6cm, α = 2.31 rad/s^2

From rotaitonal kinetmatic equation

θ = θo +wt +(1/2)αt²

θ = 0.265 +0 +(1/2)(2.31)(3.51*3.51)

θ =14.495 rad

θ = (14.495*360)/(2*3.14)

θ = 830.9⁰

x = rcosθ =6cos(830.9) =-2.14 cm

y = rsinθ =6 sin(830.9) = 5.6 cm

x–y coordinates of the chip is (-2.14 cm , 5.6 cm)