A CD has diameter 140 mm. The angular speed is about 150 RPM. Find the LS in cm/second. What is the AS in cm/second?

Question

These questions are very confusing to me and I can not seem to get the understanding of them for participation homework but I need to understand them for my quizzes. LS is linear speed, AS is angular speed.

Answer 1

C = πd

C ≈ 439.82 cm

150 rpm = 2.5 rps

LS_{at edge} = 439.82 cm / 2.5 rps

LS_{at edge} = 175.928 cm / sec

AS = (360°)(2.5) / sec

Answer 2

150 rpm = 150/60 rps = 2.5 rps. there's 60 seconds in a minute

diameter = 140 mm = 14 cm 1 cm = 10 mm

circumference = pi(d) = pi(14) cm = about 43.98 = about 44 cm

in 1 second there is 2.5 rotations so the edge of the CD moves 44/2.5 = 17.6 cm per second

LS = lateral speed of an edge of the CD = 17.6 cm/sec

angular speed or velocity is change in the angle per change in time or per second or 2pi(2.5)

= 5pi per second

or

360(2.5) = 902.5 degrees per second

the formula for AS is change in angle divided by change in time