calculate the average angular acceleration and initial angular velocity of a wheel that has w=1.5wo(initial omega) at the end of 1min and w=45rev/sec at the end of 3min

To calculate the average angular acceleration and initial angular velocity of the wheel, we need to use the formula for angular acceleration:

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

We are given that the angular velocity (ω) at the end of 1 minute (t1) is 1.5 times the initial angular velocity (wo), and the angular velocity at the end of 3 minutes (t2) is 45 revolutions per second.

Let's start by finding the change in angular velocity and the change in time:

Change in angular velocity (Δω) = ω2 - ω1
where ω2 is the angular velocity at t2 and ω1 is the angular velocity at t1.

Change in time (Δt) = t2 - t1

Given:
ω1 = 1.5wo (at t1 = 1 minute)
ω2 = 45 rev/sec (at t2 = 3 minutes = 180 seconds)

Substituting these values into the formulas, we have:

Δω = ω2 - ω1 = 45 rev/sec - (1.5wo)
Δt = t2 - t1 = 180 seconds - 60 seconds = 120 seconds

Now, we can calculate the average angular acceleration (α):

α = Δω / Δt

Substituting the values we found:

α = (45 rev/sec - 1.5wo) / 120 seconds

To find the initial angular velocity (wo), we need another equation.

From the given information, we know that ω1 = 1.5wo at t1. Since we know ω1 and wo, we can solve for wo:

1.5wo = 1.5wo (from the given equation)
wo = ω1 / 1.5

Now we have the formula to calculate the average angular acceleration and the initial angular velocity. Let's substitute the values:

Average angular acceleration (α) = (45 rev/sec - 1.5wo) / 120 seconds
Initial angular velocity (wo) = ω1 / 1.5

Please provide the specific value for ω1 to calculate the numerical result or any specific value you want to use for acceleration.