Two part angular acceleration question.

Question

The crankshaft in a race car goes from rest to 3600 rpm in 3.5 seconds.

What is the crankshaft's angular acceleration?

Express your answer using two significant figures.

How many revolutions does it make while reaching 3600 rpm

s? Express your answer using two significant figures

Express your answer using two significant figures.

Answer 1

Convert revolutions per minute into radians per second.

3600 rev/min x 2π rad x 60 s = 1.4 x 10^6 rad/s

The angular acceleration is:

α = ∆ω / ∆t = (1.4 x 10^6 rad/s - 0 rad/s) / 3.5 s = 4.0 x 10^5 rad/s²

The total angular displacement during the acceleration is:

∆θ = (ωf² - ωi²) / 2α

= ((1.4 x 10^6 rad/s)² - (0 rad/s)²) / (2 x (4.0 x 10^5 rad/s²))

= 2.5 x 10^6 rad

Convert radians into revolutions.

(2.5 x 10^6 rad) / 2π = 4.0 x 10^5 revolutions