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?
____kg·m2/s
C = pi*2r = 3.14 * 4.4 = 13.8 m. = Circumference.
Va = 3m/s * 1rev/13.8m * 6.28rad/rev = 1.37 rad/s.
Momentum = M*Va = 46 * 1.37 = 1.87 kg.rad/s.
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To find the child's angular momentum, we first need to understand the definition of angular momentum. Angular momentum is a rotational analog of linear momentum and is denoted by the symbol L. It is given by the formula:
L = I * ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
To calculate the moment of inertia, we need to determine the child's mass distribution with respect to the axis of rotation, which in this case is the center of the merry-go-round. Since the child is a point mass, the moment of inertia can be determined using the formula:
I = m * r^2
where m is the mass of the child and r is the distance of the child from the axis of rotation.
Given:
Mass of the child, m = 46 kg
Distance from the center, r = 2.2 m
Angular velocity, ω = speed / r
We can calculate the angular velocity using the given speed and distance from the center:
ω = 3 m/s / 2.2 m
Once we have the angular velocity, we can substitute the values into the formula for angular momentum:
L = (m * r^2) * ω
To find the child's angular momentum, we need to substitute the given values into the equation and perform the calculation.