# What is the component of the total angular momentum along the axle?

1. ### physicsss

319
Two lightweight rods d = 23 cm are mounted perpendicular to an axle and at 180° to each other. (Fig. 11-24). At the end of each rod is a 700 g mass. The rods are spaced 40 cm apart along the axle. The axle rotates at 41 rad/s.

http://www.geocities.com/sinceury/11-24alt.gif

(a) What is the component of the total angular momentum along the axle?

(b) What angle does the vector angular momentum make with the axle? [Hint: Remember that the vector angular momentum must be calculated about the same point for both masses.]

Last edited: Nov 2, 2004
2. ### physicsss

319
No one can help? =(

3. ### marlon

Well the quantity that you will need in order to answer your questions is the rotational inertia or moment of inertia given by:

$$I = \Sigma_{i} m_{i}r_{i}^2$$ r is distance between origin and position of the mass. Mass1 is the right hand side-rod and mass2 is the other one.

So we have (in the right units ofcourse) :

$$I = 0,7 * 0,23^2 + 0,7(0.4^2 + 0.23^2)$$

mass = 0.7 kg
d_1 = 0.23 m
d_2 = sqrt(0.4²+0.23²)

Then you need to find the designated formula's( as a function of I) for calculation your questions.

marlon

good luck

4. ### physicsss

319
So I calculated the angular around the center of mass:

L=I*w
L=0.7*v*r, and v=d*w

So L=0.7*0.23*41*sqrt(0.4²+0.23²)

So the total angular momentum is 2 times the above...but I was told that it's wrong. Any ideas?

5. ### marlon

Well that is because the I that i calculated is not with respect to the center of mass but with respect to the origin.

If we calculate with respect to the centre of mass(positioned at the intersection of the diagonal between the two masses and the axis.) you would get :

$$I = 0.7*(0.2^2 + 0.23^2) + 0.7*(0.2^2 + 0.23^2)$$

marlon

6. ### physicsss

319
If you times that by the angular speed of the rod, then you would get the answer for a, right? But I got it wrong...

7. ### marlon

yes, what should you get ??? what is the answer ??? Normally it should work

marlon

8. ### physicsss

319
I don't know, but the online homework submission thingy is not accpting my answer. =( Also, I'm getting different answers with the way you did it and the way I did it...

Last edited: Nov 4, 2004
9. ### marlon

Look you are gonna have to be more specific here. What did you get ???

marlon

10. ### marlon

Sorry, but i made a mistake in the distance from the two masses to the axis. In the formula for I the r represents the PERPENDICULAR distance to the axis so this is just 0,23 meters.

$$I = 0.7 * 0.23^2 + 0.7 * 0.23^2$$

try this one

marlon

11. ### marlon

Am i right now ???

maybe someone else can help us out here...

marlon

12. ### physicsss

319
nope =( Can someone jump in and help?

13. ### marlon

But it is just L = I * w and w = 41 rad/sec. Just multiply the two...

marlon