Question

The crankshaft in a race car goes from rest to 3000 rpm in 2.0 s.

Answer 1

Answer:

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

Answer 2

The equations are analogous to that for linear movement:
acceleration = (final velocity - initial velocity) / time
acceleration = (3000 rpm - 0 rpm) / 2.0 s
a) acceleration = 1500 rpm/s or 25 rp(s^2)
For the displacement
displacement = initial velocity*time + 0.5*acceleration*time^2
displacement = (0)*(2 s) + (0.5)(25 rps^2)*(2 s)^2
b) displacement = 50 revolutions