Answer :
Final answer:
The angular acceleration of the crankshaft that accelerates from rest to 3000 rpm in 3.4 s is approximately 29.32 rad/s² after converting the angular speed into radians per second and using the formula for angular acceleration.
Explanation:
To calculate the angular acceleration of the crankshaft that goes from rest to 3000 revolutions per minute (rpm) in 3.4 seconds, we first need to convert the angular speed to radians per second. Since 1 revolution is 2π radians and 1 minute is 60 seconds, the conversion for angular velocity ω is:
ω = 3000 rpm × (2π radians/1 revolution) × (1 minute/60 seconds)
ω = 3000 × 2π/60 rad/s
ω = 100π rad/s
The formula for angular acceleration α is:
α = (ω - ω0)/t
Since the crankshaft starts from rest, ω0 = 0. Therefore, we have:
α = (100π rad/s) / 3.4 s
α = 100π / 3.4 rad/s²
α = approx. 29.32 rad/s²
The angular acceleration of the crankshaft is approximately 29.32 rad/s².
