Prof Jeldes is out racing his 1997 Hyundai Excel while also writing the latest E

Question

Prof Jeldes is out racing his 1997 Hyundai Excel while also writing the latest EF 105 tome 'The 13 most abstract things in Excel.' Continually distracted by circular references, he drives in a circle. Help him compute the following.

A.   Cell A9 in his onboard spreadsheet says the engine speed is 4620 rpm. What is his engine speed in radians/sec? (do not enter units)  

B.   He is driving around a circle of 210 ft in diameter at a constant speed. He completes 7 laps in 26 minutes. What is his linear speed?
(include units with answer)  

C.   While driving around the circle in part B, what is the magnitude of his acceleration?
(include units with answer)  

D.   What is his angular speed while driving around the circle at a constant speed of 39 mph?
(include units with answer)

Explanation / Answer

A)
4620 rpm
= 4620 * 2*pi rad / 60 sec
= 4620*2*pi/60 rad/s
=483.8 rad/s

B)
Total distance moved = 7*2*pi*r
= 7*2*pi*(210/2)
= 4618 ft

time = 26 min

speed = 4618 ft / 26 min
= 177.6 ft/min

C)
Since speed is contant, only acceleration acting will be the centripetal acceelration
a = v^2/r
= (177.6)^2/ (210/2)
=300.4 rad/s^2

D)
R = 105 ft
V= 39 mph = 39*5280 ft/s = 205920 ft/s
W = V/R
= (205920)/(105)
= 1961 rad/s

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