How to Calculate Force and Angular Acceleration in a Rotating System?

[bionut]

Hi, I have the following q's. I can get to through most of it but I seem to get confused with computing the last part and get the wrong answer... can anyone help?

Q. The knee extensors insert on the tibia at an angle of 30degree angle at a distance of 3cm from the axis of rotation at the knee. HOw much force must the kneww extensors exert to produce an angular accelartion at the knee of 1 rad/s (squared) if the mass of the lower leg/foot is 4.5 kg and k= 23cm?

Known:

d=0.03m
$\alpha$= 1 rad/s (squared)
m= 4.5 kg
K = 0.23m

Soltuion: Using 2nd Newton angular law of motion: T=I$\alpha$ = Fd=mk(squared)$\alpha$

(F sin 30N) x (0.03m) = (4.5kg) x (0.23m)squared x (1 rad/s squared)
-0.03F=0.24
F= 0.24/0.03
F=0.0072N ... whichis wrong ? any ideas what I did wrong ;-(

 

[Spinnor]

You wrote,

"F= 0.24/0.03
F=0.0072N "

how did you get from the top line to the next? A picture would help, you have to use the 30 degrees I'm guessing but why not cos(30)?

Good luck!