1. The problem statement, all variables and given/known data The 1.6kg, 20cm diameter disk in the figure below is spinning at 240rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 3.5s? http://i241.photobucket.com/albums/ff4/alg5045/p13-69.gif 2. Relevant equations 3. The attempt at a solution I know a free body diagram should be drawn for the disk to take all of the forces into account. I know there's the weight pulling down and the frictional force is acting to the right, but I don't know how to set up a solvable equation.
Use 1.6kg, 20cm diameter disk to determine the moment of inertia. The friction force behaves as a torque with moment r and force f. Torque/(moment of inertia) = angular acceleration then use the appropriate equation of motion for rotation to determine the time to decelerate from the initial angular velocity to stop in 3.5 s. See - http://hyperphysics.phy-astr.gsu.edu/hbase/mi
One is given time, and ask what magnitude of force is require to bring the disk to standstill ([itex]\omega[/itex] = 0) in that time. Use the change in angular velocity and time to find the constant angular acceleration. Applying an external force (friction) will cause the rotational mass to decelerate. One must apply the appropriate equation(s) of motion, e.g. [itex]0 = \omega_0\,+\,\alpha\,t[/itex], where [itex]\omega_0[/itex] is the initial angular velocity, and [itex]\alpha[/itex] is the angular acceleration (or deceleration if negative). With the angular acceleration (or deceleration), use the relationship between torque and moment of intertia. Then knowing the net torque required to decelerate the disk, then find the necessary friction force applied at the appropriate moment arm (radius of disk).
I did the following... I=m(r^2)=.016. I then converted revolutions per minute into radians per second = 25.133. Then I found angular acceleration by using delta w/delta t = 7.181, and finally I found the torque = I(alpha) = .115. I'm still unsure about finding the friction.
That formula is incorrect for a solid disk. To relate torque to friction force, realize that the friction force acting with a moment arm = r creates the given torque (as Astronuc had stated).
Ok so instead I = .032 and T = .23. Then I use T = rF (I think) and I solved for F to get 2.3, but it wasn't right.