I child with a mass of 20kg,hops on a merry go round with moment of intertia of 1000kg and radius of 7m.if it takes the child time T to move 360degrees ,relative to the ground at 6m away from the center,what is the angle covered relative to the ground

To find the angle covered by the child relative to the ground, we need to use the concept of angular displacement.

Angular displacement (θ) is given by the formula:

θ = s / r

Where:
θ is the angular displacement,
s is the arc length (distance traveled on the circumference), and
r is the radius of the merry-go-round.

In this case, the child travels 360 degrees, which is equivalent to a full circle on the merry-go-round. The circumference of a circle is given by the formula:

C = 2πr

So, the arc length traveled by the child is:

s = (360 degrees / 360 degrees) * (2π * radius)

Now, we have the values needed to calculate the angle covered relative to the ground.

Given:
Child's mass (m) = 20 kg
Moment of inertia (I) = 1000 kg*m^2
Radius (r) = 7 m
Time (T) = time taken to move 360 degrees

First, we need to calculate the angular velocity (ω) using the formula:

ω = Δθ / Δt

Since the child took time T to move 360 degrees (Δθ = 360 degrees), we have:

ω = 360 degrees / T

Next, we can calculate the linear velocity (v) of the child using the formula:

v = ω * r

Now that we have the linear velocity, we can calculate the arc length traveled by the child using the formula:

s = v * Δt

Finally, we can calculate the angle covered by the child relative to the ground using the formula we mentioned earlier:

θ = s / r

Plugging in the values and following the calculations above will give us the angle covered relative to the ground by the child.