The rotation rate (number of rotations per minute) of a car’s engine\'s cranksha

Question

The rotation rate (number of rotations per minute) of a car’s engine's crankshaft is displayed in the dashboard by the tachometer (see Figure below). It has markings indicating a safe range of rotations. If the angular velocity of the crankshaft is 700 rad/s what will the car’s tachometer indicate? If the safe range of the crankshaft rotation should be less then 5700rev/min (RPM) is it safe to operate the car at this RPM? What is the linear velocity of points on the surface of the crankshaft if its radius is 5cm? What is their centripetal acceleration? What is the period of the rotations?

Explanation / Answer

a)

angular velocity

W=700 rad/s

1 rad/sec =(60/2pi) rpm

W=700*(60/2pi) =6684.5 rpm

So it is greater than safe range ,so it not safe to operate the car at this rpm

b)

Linear velocity

V=RW=0.05*700

V=35 m/s

c)

centripetal acceleration

a=V2/r =352/0.05

a=24,500 m/s2

d)

Period

T=2pi/W =2pi/700

T=8.976*10-3 s or 8.976 ms

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