Essentially, I am trying to determine the force that must be applied to a rotating disc to that stop that disc from rotating in a certain time period.
The disc is rotating at 5800 rpm, the disc has a radius of 5 inches, and a thickness of 0.087 inches. The disk is made of titanium (density of 4507 kg/m^3). The time required to stop the disk is 0.005 seconds.
K = 1/2*I*ω^2 ; I = 1/2*m*r^2 ; -------> K = 1/2(1/2*m*r^2)*ω^2
The Attempt at a Solution
Knowing ω = (2∏) / T , I was able to calculate ω to be ω= 607.375 rad/sec
Volume of the disc = V = ∏r^2h, which leads to V = 1.1197 E-4 m^3
Using the density, I found the mass of the disk to be m = 0.50465 kg.
Plugging all of this into equation above for kinetic energy, I found K to be K = 750.7 joules
It's been a while since I took a dynamics course. How can I determine the force necessary (I guess I'm kind of assuming a friction-like force such as a break being applied) to stop the disc from spinning in 0.005 seconds? I know I'll need an integral, but I forget the exact formula and steps necessary to finish up this problem.