A large merry-go-round completes one revolution every 10.5 s. Compute the acceleration of a child seated on it, a distance of 5.20 m from its center. what is the magnitude?

a= w^2*r=(2PI/10.5)^2 * 5.2

To find the acceleration of the child seated on the merry-go-round, we need to use the formula for centripetal acceleration:

a = (v^2) / r

where:
a = acceleration
v = velocity
r = radius

First, let's find the velocity of the child. The velocity is equal to the circumference of the circle divided by the time it takes to complete one revolution.

v = (2 * π * r) / t

Substituting the values:
r = 5.20 m (distance from the center)
t = 10.5 s (time taken for one revolution)

v = (2 * π * 5.20) / 10.5

To calculate the magnitude of the acceleration, we will substitute this value into the centripetal acceleration formula.

a = (v^2) / r

Substituting the values:
v = [(2 * π * 5.20) / 10.5]
r = 5.20 m

a = [(2 * π * 5.20) / 10.5]^2 / 5.20

Now we can calculate the magnitude of the acceleration.

To compute the acceleration of a child seated on a merry-go-round, we need to use the formula for centripetal acceleration:

a = (v^2) / r

where "a" represents the acceleration, "v" represents the velocity, and "r" represents the radius of the circular motion.

Since the merry-go-round completes one revolution every 10.5 s, we can calculate the velocity by dividing the circumference of the circle (2 * π * r) by the time taken:

v = (2 * π * r) / t

Substituting the given values, we have:

v = (2 * 3.14 * 5.20 m) / 10.5 s

Now we can calculate the velocity:

v ≈ 3.08 m/s

Next, we can substitute the velocity and radius into the formula for centripetal acceleration:

a = (3.08 m/s)^2 / 5.20 m

Now we can calculate the acceleration:

a ≈ 1.83 m/s^2

Therefore, the magnitude of the acceleration of the child seated 5.20 m from the center is approximately 1.83 m/s^2.