# Moments and Pivots

1. May 11, 2017

### Sarahborg

1. The problem statement, all variables and given/known data
A uniform board of length 90cm is pivoted at a hinge at one end. It is kept level by an upward vertical force T applied at the opposite end. The weight of the board is 6N. Take moments about the hinge to find T when the board is level.

2. Relevant equations
Moment = Force x Perpendicular distance

3. The attempt at a solution
I tried doing 45 x 6 = 270, and then 270/90 which is 3N. I think it's wrong though (I got the 45 by dividing 90 by 2)

2. May 11, 2017

### BvU

Hello Sarah,

Much better !
What makes you doubt the result ?
Your moment balance looks like ( -45 * 6 + 90 * 3) cm * N and that is zero, so no angular acceleration.

3. May 11, 2017

### CWatters

+1

Welcome to the forum. It looks right to me as well.

4. May 11, 2017

### Sarahborg

Thank you very much

5. May 11, 2017

### Sarahborg

How do you calculate angular acceleration, because we haven't covered it yet, and got curious.

Thank you very much for your help :)

6. May 11, 2017

### BvU

Pardon the link: there is a parallel between linear motion and angular motion.

7. May 11, 2017

### CWatters

Although in this case there is no angular acceleration because you were asked to arrange for the net torque to sum to zero. See also Newton's laws.

8. May 12, 2017

Thanks

9. Jun 4, 2017

### Sarahborg

How are Newton's Laws related to angular acceleration?

Thanks

10. Jun 4, 2017

### BvU

Have you come to the conclusion the answer you found in post #1 is correct ? Oh well, I hinted as much in post #2.

For Newton we have $$\vec F = m\vec a$$ and the (almost carbon copy) equivalent in angular motion is $$\vec \tau = I\vec \alpha$$
(see table 1 here)
$\vec \tau$ is the torque
$I$ is the moment of inertia
$\vec \alpha$ is the angular acceleration