Angular Acceleration and Revolutions

The crankshaft in a race car goes from rest to 3500 rpm in 3.5 seconds.

What is the crankshaft’s angular acceleration?

Known Variables:

time: 3.5 seconds

angular frequency(ω): 3500 rpm

We know that the angular acceleration formula is as follows:

α= ω/t

First we need to convert ω into proper units which is in radians/second.

3500 rpm x 2π/60 = 366.52  rad/s²

since we found ω, we can now solve for the angular acceleration (γ= ω/t).

α= 366.52/ 3.5
= 104 rad/s²

or in two significant figures, 100 rad/s²

α= 100 rad/s²

How many revolutions does it make while reaching 3500 rpm?

First is to find the total angular displacement during the acceleration:

angular displacement (θ) = (1/2)αt²

=1/2     x     (    104 rad/s² *(3.5s)² )

θ = 637 rad

number of Revolutions (n) = θ/2π

= 637 rad/2π = 100 revs

n= 100 revolutions