To find how fast you spin in rad/s, you need to use the conservation of angular momentum principle. The principle states that the total angular momentum before an event (turning on the hard drive) is equal to the total angular momentum after the event.
The total angular momentum before the event is 0, because both you and the hard drive are at rest. So, we have:
0 = L_disk + L_astronaut
L_disk is the angular momentum of the disk, which you have found to be 0.0095 kg*m^2/s. L_astronaut is the angular momentum of the astronaut, which we need to find.
To find the angular momentum of the astronaut, we can use the following formula:
L_astronaut = I_astronaut * ω_astronaut
where I_astronaut is the moment of inertia of the astronaut, and ω_astronaut is the angular velocity in rad/s.
We can approximate the astronaut as a uniform sphere of radius 30 cm (0.3 m) and mass 70 kg. The moment of inertia of a uniform sphere is given as:
I_astronaut = (2/5) * M_astronaut * R_astronaut^2
I_astronaut = (2/5) * 70 kg * (0.3 m)^2
I_astronaut ≈ 5.04 kg*m^2
Now, we can find the angular velocity (ω_astronaut) by rearranging the angular momentum formula:
0 = 0.0095 kg*m^2/s + 5.04 kg*m^2 * ω_astronaut
ω_astronaut = -0.0095 kg*m^2/s / 5.04 kg*m^2
ω_astronaut ≈ -0.0019 rad/s
So, you will spin at approximately -0.0019 rad/s. The negative sign means that you will spin in the opposite direction of the hard drive.
You are a 70 kg 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? Approximate yourself as a uniform sphere of radius 30 cm. What formula do I use?
I found the Angular momentum of the disk (.0095) and its mass (.0167).
1 answer