Two astronaut, as shown in the figure, each having a mass of 62.0 kg, are connected by a 12.00 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum
Their angular velocity about the center of rotation is
w = V/R = 5.0/6 = 0.833 rad/s
The angular momentum is
2*M*w*R^2
where M is the mass of a single astronaut
To calculate the magnitude of the angular momentum, we need to use the formula:
L = mvr
Where:
L is the angular momentum
m is the mass of the astronaut
v is the speed of the astronaut
r is the distance of the astronaut from the center of rotation
In this case, since the astronauts are moving in circles around the point halfway between them, the distance from the center of rotation is half of the rope length:
r = 12.00 m / 2 = 6.00 m
Now, we can plug in the given values into the formula to calculate the magnitude of the angular momentum:
L = (62.0 kg) * (5.00 m/s) * (6.00 m)
L = 1860 kg m²/s
Therefore, the magnitude of the angular momentum is 1860 kg m²/s.