A child with a mass of 46 kg is riding on a merry-go-round. If the child has a speed of 3 m/s and is located 2.2 m from the center of the merry-go-round, what is the child's angular momentum?
____kg2/s
v = omega r = 3
so
omega = 3/2.2
I = m r^2 = 46 * 2.2^2
L = I omega = 46 * 2.2^2 * 3/2.2
= 46 * 2.2 * 3
To find the child's angular momentum, we need to use the equation:
Angular momentum (L) = moment of inertia (I) * angular velocity (ω)
The moment of inertia depends on the mass and the distance from the center of rotation. The formula for the moment of inertia of a point mass rotating about a fixed axis is:
I = m * r^2
Where:
- I is the moment of inertia
- m is the mass of the object
- r is the distance between the object and the axis of rotation
In this case, the child's mass is given as 46 kg and the distance from the center is 2.2 m. Therefore, we can calculate the moment of inertia:
I = 46 kg * (2.2 m)^2
I = 46 kg * 4.84 m^2
I = 222.64 kg*m^2
Angular velocity (ω) is the rate at which the child is moving in a circular path. It is related to linear velocity (v) and radius (r) by the equation:
v = ω * r
Rearranging the equation, we can find the angular velocity:
ω = v / r
ω = 3 m/s / 2.2 m
ω = 1.36 rad/s
Now, we can calculate the angular momentum:
L = I * ω
L = 222.64 kg*m^2 * 1.36 rad/s
L ≈ 302.7784 kg*m^2/s
Therefore, the child's angular momentum is approximately 302.7784 kg*m^2/s.