Answer :
If the pulley rotates at a rate of 3 revolutions per second, then the period T of movement is [tex]\frac{1}{3}s[/tex]
a) calculate the angular velocity:
[tex]\omega=\frac{2 \pi}{T}\\ \\ \omega=\frac{2 \pi}{\frac{1}{3}}=6 \pi \ rad/s[/tex]
b) calculate the linear velocity:
[tex]v=\frac{2 \pi R}{T}=\frac{2 \pi.8}{\frac{1}{3}}=24 \pi \ in/s \approx 75,36 \ in/s[/tex]
Remember: 1 in/s = 300 ft/h
So, 75,36 in/s = 22,608 ft/h
a) calculate the angular velocity:
[tex]\omega=\frac{2 \pi}{T}\\ \\ \omega=\frac{2 \pi}{\frac{1}{3}}=6 \pi \ rad/s[/tex]
b) calculate the linear velocity:
[tex]v=\frac{2 \pi R}{T}=\frac{2 \pi.8}{\frac{1}{3}}=24 \pi \ in/s \approx 75,36 \ in/s[/tex]
Remember: 1 in/s = 300 ft/h
So, 75,36 in/s = 22,608 ft/h
