The crankshaft of an engine increases its spin from 1,200 rpm to 1,500 rpm in 0.50 s. What is its angular acceleration

300rev/min / (1/120 min) = 36000 rev/min^2

Now you can convert that to whatever units you like.

Remember: 2pi radians/rev

To find the angular acceleration, we can use the following formula:

Angular acceleration (α) = (final angular velocity - initial angular velocity) / time

Given that the initial angular velocity (ω1) is 1,200 rpm, the final angular velocity (ω2) is 1,500 rpm, and the time (t) is 0.50 seconds, we can substitute these values into the formula:

α = (ω2 - ω1) / t
= (1500 rpm - 1200 rpm) / 0.50 s

Let's calculate it:

α = (300 rpm) / 0.50 s

Now, we need to convert rpm to radians per second (rad/s) since the standard unit for angular acceleration is rad/s^2. To do this, we know that 1 revolution = 2π radians, and 1 minute = 60 seconds. Therefore:

α = (300 rpm) / 0.50 s * (2π radians / 1 revolution) * (1 revolution / 60 s)
≈ π rad/s^2

So, the angular acceleration of the crankshaft is approximately π rad/s^2.

To find the angular acceleration, we need to use the formula:

Angular acceleration (α) = (change in angular velocity (Δω)) / (change in time (Δt))

The change in angular velocity (Δω) can be calculated by subtracting the initial angular velocity (ω1) from the final angular velocity (ω2):

Δω = ω2 - ω1

Given:
Initial angular velocity (ω1) = 1,200 rpm
Final angular velocity (ω2) = 1,500 rpm
Change in time (Δt) = 0.50 s

First, let's convert the angular velocities from rpm to radians per second (rad/s). Since 1 revolution is equal to 2π radians, we have:

ω1 = (1,200 rpm) * (2π rad/1 min) * (1 min/60 s) = 40π rad/s
ω2 = (1,500 rpm) * (2π rad/1 min) * (1 min/60 s) = 50π rad/s

Now, we can calculate the change in angular velocity:

Δω = 50π rad/s - 40π rad/s = 10π rad/s

Next, we can substitute the values into the formula for angular acceleration:

α = (Δω) / (Δt) = (10π rad/s) / (0.50 s) = 20π rad/s²

Therefore, the angular acceleration of the crankshaft is 20π rad/s².