The crankshaft in a race car goes from rest to 3000 rpm in 2.0 s. a. what is the crankshaft's angular acceleration? b. how many revolutions does it make while reaching 3000 rpm?

a.  157 rad/s²

b. 50 revolutions

Explanation:

Initial angular velocity, u = 0

Final v = 3000 rpm = 3000 × 2π/60 rad/s= 314 rad/s

time, t = 2.0 s

a. angular acceleration is given by first equation of rotational motion:

α = (v-u)/t = (314 rad/s-0)/ 2.0 s = 157 rad/s²

b. number of revolutions made before reaching final angular velocity of 3000 rpm. Time taken = 2.0 s.

Use second equation of rotational motion:

θ = u t + 0.5 α t²

⇒ θ = 0 + 0.5 × 157 rad/s² × (2.0 s.)² = 314 rad

⇒n ( number of revolutions) =  θ / 2π = 314/ 2π = 50 revolutions

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