A centrifuge in a medical laboratory rotates at an angular speed of 3800 rev/min. When switched off, it rotates through 46.0 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge. in

1 rad/s2

The average speed while it comes to rest is 1900 rev/min. At that average rate, the centrifuge takes 46/1900 min, which is 14.53 seconds, to stop.

To get the angular deceleration rate, convert 3800 dev/mom to rad/s, and then divide by 14.53 s.

To find the constant angular acceleration of the centrifuge, we can use the formula:

θ = ω₀t + (1/2)αt²

Where:
θ = number of revolutions (46)
ω₀ = initial angular speed (3800 rev/min)
t = time taken to stop spinning
α = angular acceleration (what we want to find)

First, let's convert the initial angular speed into radians per second:
ω₀ = 3800 rev/min
1 rev = 2π radians
So, ω₀ = 3800 rev/min * (2π rad/1 rev) * (1 min/60 sec) = 400π rad/sec

Now, let's convert the number of revolutions to radians:
θ = 46 rev * 2π rad/1 rev = 92π rad

With these values, our equation becomes:
92π = (400π)t + (1/2)αt²

Since the centrifuge stops spinning, its final angular speed is 0 rad/s. Therefore:
ω = ω₀ + αt
0 = 400π + αt

Now we have two equations:
92π = (400π)t + (1/2)αt²
0 = 400π + αt

Let's solve the second equation for t:
αt = -400π
t = -(400π) / α

Substitute this value of t into the first equation:
92π = (400π)(-(400π)/α) + (1/2)α(-(400π)/α)²
92π = -(160,000π²)/α + (1/2)(160,000π²)/α²
92π = -(160,000π²)/α + (80,000π²)/α²

Multiplying both sides by α² to eliminate the denominator:
92πα² = -(160,000π²) + (80,000π²)
92πα² = -80,000π²
92α² = -80,000
α² = -80,000/92
α² ≈ -869.57

Taking the square root of both sides, we get:
α ≈ √(-869.57)
α ≈ ±29.50

Since α represents angular acceleration, it cannot be negative. Therefore, the constant angular acceleration of the centrifuge is approximately 29.50 rad/s².