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?
time: 3.5 seconds
angular frequency(ω): 3500 rpm
We know that the angular acceleration formula is as follows:
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