You are a 70kg astronaut floating at rest in zero gravity holding your laptop. Your hard drive turns on (increasing from 0 to 5400 rpm). How fast do you spin in rad/s?
I'm not sure how to understand this problem. What procedure should I use to solve this?
It is a silly question attempting to demonstrate the conservation of angular momentum. To do that, one would have to know the momentu of inertia of the spinning part of the hard drive. You do not know that. It is not given. I have no explanation for what your teacher might be thinking.
To solve this problem, you need to apply the conservation of angular momentum. Angular momentum is a property of rotating objects and is given by the equation:
Angular momentum (L) = Moment of inertia (I) * Angular velocity (ω)
In this case, the astronaut and the laptop are initially at rest, so the total angular momentum is zero. When the hard drive turns on, it starts rotating at a certain angular velocity. As there is no external torque acting on the system, the angular momentum should remain conserved.
To find the final angular velocity, you need to equate the initial and final angular momenta. First, you need to determine the moment of inertia (I) of the system. The moment of inertia depends on the mass distribution and shape of the objects involved in rotation.
Since we don't have the exact shape or size of the laptop, we will consider it as a point mass rotating about an axis. The moment of inertia for a point mass rotating about an axis is given by:
I = mass (m) * radius of rotation (r)^2
In this case, the mass (m) is 70 kg, and the radius of rotation (r) is the distance between the laptop and the axis of rotation, which we assume to be negligible.
Therefore, I = 70 kg * 0^2 = 0 kg·m²
Next, we can set the initial and final angular momenta equal to each other and solve for the final angular velocity (ω).
Initial angular momentum (L_initial) = Final angular momentum (L_final)
0 = I * 0 + I_final * ω_final
Since I = 0 kg·m², the final angular velocity (ω_final) would be undefined or indeterminate in this case.
Thus, in this specific scenario, the calculation for the final angular velocity cannot be determined.