Answer:
As per the statement: A point 5 cm from the center of the disc is spinning at a rate of 4000 revolutions per minute
To find the linear speed in (km/hr):
Use conversion:
1 km = 100000 cm
1 hr = 60 min
radius of a disc(r) = a point from a center of a disc = 5 cm = [tex]\frac{5}{100000} = 0.00005 km = 5 \times 10^{-5}[/tex]
Angular speed of the drive is given by:
[tex]v = \frac{2 \pi r}{T}[/tex] where v is the angular speed and T is the time for 1 revolution.
[tex]T = \frac{1}{n}[/tex] ; where n is the revolution per min.
Substitute the given values we have;
[tex]v = \frac{2 \pi \cdot 5 \cdot 10^{-5}}{\frac{1}{4000}}[/tex]
or
[tex]v = 4000 \cdot 2 \pi \cdot 5 \cdot 10^{-5}[/tex]
Simplify:
[tex]v = 4 \times 10^{-1} \pi[/tex] km\min
1 hour = 60 minutes.
then;
[tex]v = 60 \times 4 \times 10^{-1} \pi= 24 \times 10^{-1} = 24 \pi km/hr[/tex]
therefore, the linear speed in km/hr is, [tex]24 \pi[/tex]
