Assume an aluminum platter that is 3.5 inches in diameter, 1mm thick, and spinning at 5400 rpm. Treat the platter as a solid disk. What is its angular momentum in kg-m/s?
angular momentum = Iw. However, moment of inertia requires mass, and I am not given mass.
How do I find the mass?
Thank you.
2700 kg/m^3 = density of Al
volume = pi R^2 *thickness
I = (1/2) m R^2
USE METERS and kg
Is it 9.36 * 10^-3 (angular momentum)? That seems awfully small
Yep! It is! Thank you!
To find the mass of the aluminum platter, you can use its dimensions and the density of aluminum. The volume of the platter can be calculated using its dimensions (diameter and thickness) and then multiplied by the density of aluminum to find the mass.
Step 1: Calculate the volume of the platter:
The volume of a solid disk can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height (or thickness) of the disk.
Given that the diameter of the platter is 3.5 inches, the radius would be half of that (1.75 inches or 0.04445 meters). The height is given as 1mm, which can be converted to meters as 0.001 meters.
V = π * (0.04445 m)^2 * 0.001 m
Step 2: Find the density of aluminum:
The density of aluminum can be found in reference materials or online sources. The density of aluminum is approximately 2,700 kg/m^3.
Step 3: Calculate the mass of the platter:
Using the obtained volume and the density of aluminum, we can calculate the mass using the formula: mass = volume * density.
mass = V * density
Finally, step 4: Plug in the values to calculate the mass of the platter and proceed with the calculation of angular momentum using the formula angular momentum = moment of inertia * angular velocity.
Please note that I've provided the steps to find the mass, but to directly answer your original question, I would need the mass of the platter to calculate the angular momentum.