HELP: Angular Momentum and Torque in a Rotating Disk System

[fball558]

HELP: angular momentum??

1. Homework Statement

A uniform solid disk with radius 10 cm has mass 0.7 kg (moment of inertia I = ½MR2). A constant force 12 N is applied as shown. At the instant shown, the angular velocity of the disk is 40 radians/s in the -z direction (where +x is to the right, +y is up, and +z is out of the page, toward you). The length of the string d is 15 cm.


At this instant, what are the magnitude and direction of the angular momentum about the center of the disk?


What are the magnitude and direction of the torque on the disk, about the center of mass of the disk?


3. The Attempt at a Solution

i know both of these have a -z direction. for finding the angular momentum i used
(MR^2/2)W (.7*.1^2/2) * (2(pi)/40) = 5.498e-4
then to find torque i used RF where F is tension force got this by (M*F) = (.7*12) = 8.4
then R*(8.4) = .1*8.4 = .84
these are the wrong answers.
what did i do wrong??

 

[NateD]

Answer: For the angular momentum, you need to use the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. For this problem, I = 0.35 kg m2 and ω = -40 rad/s, so the angular momentum is L = 0.35(-40) = -14 kg m2/s. The direction is -z. For the torque, you need to use the formula τ = rF, where r is the length of the string and F is the applied force. For this problem, r = 0.15 m and F = 12 N, so the torque is τ = (0.15)(12) = 1.8 Nm. The direction is also -z.