A children merry go round in the consist of 300 kg solid horizontal disk of radius 8.5 m. It rotates at a speed of .25 revolution per second while a person of mass 150 km takes a ride at the edge of the disk. How fast will the disk be rotating if the person walks 4m along the radius towards the center?

V=0.25rev/s * 6.28rad/rev = 1.57 rad/s.

Note: The person's distance from the center does not affect the angular velocity. But the linear velocity decreases as the person walks toward the center.

To solve this problem, we need to apply the principle of conservation of angular momentum.

The angular momentum of the system (disk + person) is given by:

L1 = I1 * ω1

Where:
L1 = angular momentum of the system before the person moves (initial)
I1 = moment of inertia of the system before the person moves (initial)
ω1 = angular velocity of the system before the person moves (initial)

After the person moves towards the center, the angular momentum of the system becomes:

L2 = I2 * ω2

Where:
L2 = angular momentum of the system after the person moves (final)
I2 = moment of inertia of the system after the person moves (final)
ω2 = angular velocity of the system after the person moves (final)

According to the conservation of angular momentum, L1 = L2.

Now, let's calculate the initial angular momentum (L1) and final angular momentum (L2):

L1 = I1 * ω1
L2 = I2 * ω2

The moment of inertia (I) of a solid disk is given by the formula:

I = (1/2) * m * r^2

Where:
m = mass of the disk
r = radius of the disk

So, the initial moment of inertia (I1) is:

I1 = (1/2) * m * r^2

The final moment of inertia (I2) is:

I2 = (1/2) * m * (r - d)^2

Where:
d = distance moved by the person along the radius towards the center

Now, we can rewrite the angular momentum equation using the moment of inertia formulas:

(L1) = (1/2) * m * r^2 * ω1
(L2) = (1/2) * m * (r - d)^2 * ω2

Since L1 = L2, we can equate the two equations:

(1/2) * m * r^2 * ω1 = (1/2) * m * (r - d)^2 * ω2

Let's now substitute the given values into the equation and solve for ω2:

Mass of the disk (m) = 300 kg
Radius of the disk (r) = 8.5 m
Initial angular velocity (ω1) = 0.25 revolution/second
Distance moved by the person along the radius towards the center (d) = 4 m

Plugging in these values:

(1/2) * 300 kg * (8.5 m)^2 * 0.25 revolution/second = (1/2) * 300 kg * (8.5 m - 4 m)^2 * ω2

Simplifying the equation further, we have:

(1/2) * 300 kg * (8.5 m)^2 * 0.25 revolution/second = (1/2) * 300 kg * (4.5 m)^2 * ω2

Now, we can solve for ω2 by canceling out the common terms:

(8.5 m)^2 * 0.25 revolution/second = (4.5 m)^2 * ω2

Now, let's calculate ω2:

(8.5 m)^2 * 0.25 revolution/second = (4.5 m)^2 * ω2

72.0625 revolution/second = 20.25 m^2 * ω2

Dividing both sides by 20.25 m^2:

72.0625 revolution/second / 20.25 m^2 = ω2

ω2 ≈ 3.56 revolution/second

Therefore, the disk will be rotating at a speed of approximately 3.56 revolutions per second after the person walks 4 meters along the radius towards the center.