A Blu-ray disc is approximately 13 centimeters in diameter. The drive motor of a Blu-ray player is able to rotate up to 10,000 revolutions per minute. (a) Find the maximum angular speed (in radians per second) of a Blu-ray disc as it rotates. (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. rad/sec (b) Find the maximum linear speed (in meters per second) of a point on the outermost track as the disc rotates. (Round your answer to two decimal places.) m/sec

(a) ω = 1047.62 rad/sec

(b) v = 68.10 m/sec

Step-by-step explanation:

(a) Maximum angular speed, ω = θ(radians or revolutions)/t(secs)

θ = Angle of rotation,

t = time(secs)

ω = 10000revs/min

But 1 rev = 2Π radians = 2 * 22/7 = 44/7

1 rev = 44/7 radians

So, 10000 revs = = 62857.143 radians

1 minute = 60 seconds

Therefore,

ω =

ω ≅ 1047.62 rad/sec

(b) Maximum linear speed, v = rω

radius, r = diameter/2 = 13cm/2

r = 6.5cm

But 100cm = 1m

Therefore, 6.5cm = 6.5m/100

Thus, radius, r = 0.065 meters

Maximum speed, v = 0.065 * 1047.62 = 68.0953

v ≅ 68.10 m/sec

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47