# Pendulum and Torque

1. Jun 23, 2007

### kiwikahuna

1. The problem statement, all variables and given/known data

A) A simple pendulum consits of a 2.1 kg point mass hanging at the end of a 4.3long light string that is connected to a pivot point.
a. Calculate the magnitude of the torque (due to the force of gravity) around this pivot point when the string makes a 4.6 degree angle with the vertical.
B) Repeat this calculation for an angle of 15.6 degrees.

2. Relevant equations
torque = mglsin(theta)

3. The attempt at a solution
I think the above equation is the right equation to use in this problem but I'm not sure what to plug in for theta. Is it the angle that's given or do I have to add 90 degrees to the given angle because the string makes the angle with the vertical? I have the same question for Part B as well. Thank you in advance for any help/advice.

2. Jun 23, 2007

### mjsd

first draw a force diagram. next think about how one may derive the equation torque = mgl.sin(theta), ... ok... mg is a force (which is a vector). now what does mgl.sin(theta) looks like? yes.. the magnitude of a cross product of some sort eh... so which are your two vectors? I have already identify one for you.
remember in general torque is given by
$$\vec \tau= \vec R \times \vec F$$
so what is your R in this case?

once you have identified your two vectors... then use your knowledge of the cross product which tells you that the angle (theta) is the (smaller) angle between the two vectors.

Last edited: Jun 23, 2007
3. Jun 23, 2007

### kiwikahuna

Would my R be the tension from the string [lsin(theta)]?

Could you explain to me more about what you mean when you say "the smaller angle?"

I'm not very familiar with the cross product although we did learn about the dot product.

4. Jun 24, 2007

### Staff: Mentor

$\vec{R}$ is the position vector of the pendulum bob; it is parallel to the string and has a magnitude equal to the length of the string. The angle you need is that between the position vector (the string) and the force (gravity, which is vertical). So the theta needed is the given angle that the string makes with the vertical.

Any two vectors (A & B) in a plane make some angle with respect to each other. You can describe the angle as A to B or B to A. One of those angles will be less than 180 degrees, the other greater. (But the sine of either angle will have the same magnitude.)

5. Jun 25, 2007

### mjsd

if $$\vec A, \vec B$$ are two vectors, then the magnitude of the cross product between A and B is given by
$$|\vec A \times \vec B| = |\vec A||\vec B|\;\sin \;\theta$$
where theta is the angle between the two vectors.

I was trying to point out to you where the sin theta actually comes from and hopefully from that you can deduce which angle to use.

6. Jun 25, 2007

### kiwikahuna

Thank you to both Doc Al and mjsd. I think I finally got it!