Answer:
(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 = [tex]\frac{10000*44}{7}= \frac{440000}{7}[/tex] = 62857.143 radians
1 minute = 60 seconds
Therefore,
ω = [tex]\frac{62857.143rads}{60secs} = 1047.619 radians/sec[/tex]
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
