In a playground, there is a small merry-go-round of radius 1.20 m and mass 190 kg. Its radius of gyration (see Problem 85 of Chapter 10) is 91.0 cm. A child of mass 44.0 kg runs at a speed of 4.50 m/s along a path that is tangent to the rim of the initially stationary merry-go-round and then jumps on. Neglect friction between the bearings and the shaft of the merry-go-round.
b) Calculate the magnitude of the angular momentum of the child, while running, about the axis of rotation of the merry-go-round
Cancer
Where can I find the answers to this damn website?!?!?!?!?!?
dsf
To calculate the magnitude of the angular momentum of the child while running about the axis of rotation of the merry-go-round, we need to use the formula for angular momentum:
L = I * ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
The moment of inertia can be calculated using the formula I = m * r^2, where m is the mass and r is the radius of gyration. In this case, the radius of gyration is given as 91.0 cm, which is 0.91 m.
First, let's calculate the moment of inertia of the merry-go-round itself:
I_merry = m_merry * r_merry^2
= 190 kg * (1.20 m)^2
Next, let's calculate the moment of inertia of the child while running:
I_child_running = m_child * r_child_running^2
= 44.0 kg * (0.91 m)^2
Now, let's calculate the angular velocity of the child running along the path tangent to the rim of the merry-go-round. Since the child is running in a tangential path, the tangential speed v_tan is equal to the radius of the merry-go-round multiplied by the angular velocity.
v_tan = r_child_running * ω_child_running
Rearranging the equation, we have:
ω_child_running = v_tan / r_child_running
Given that the child's speed is 4.50 m/s and the radius of gyration is 0.91 m, we can calculate the angular velocity:
ω_child_running = 4.50 m/s / 0.91 m
Now, we have all the necessary values to calculate the angular momentum of the child while running:
L_child_running = I_child_running * ω_child_running
Plugging in the values we have determined:
L_child_running = (44.0 kg * (0.91 m)^2) * (4.50 m/s / 0.91 m)