Finding upward force to keep a 90cm pivoted board level

[Sarahborg]

Homework Statement

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.

Homework Equations

Moment = Force x Perpendicular distance

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)

 

[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.

 

[CWatters]

+1

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

 

[Sarahborg]

+1

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

Thank you very much

 

[Sarahborg]

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

Thank you very much for your help :)

 

[BvU]

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

 

[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.

 

[Sarahborg]

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

Thanks

 

[Sarahborg]

How are Newton's Laws related to angular acceleration?

Thanks

 

[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)https://www.boundless.com/physics/textbooks/boundless-physics-textbook/uniform-circular-motion-and-gravitation-5/angular-vs-linear-quantities-59/angular-vs-linear-quantities-272-6253/in angular motion is $$ \vec \tau = I\vec \alpha $$
(see table 1 https://www.boundless.com/physics/textbooks/boundless-physics-textbook/rotational-kinematics-angular-momentum-and-energy-9/problem-solving-88/problem-solving-techniques-332-6291/)
$\vec \tau$ is the torque
$I$ is the moment of inertia
$\vec \alpha$ is the angular acceleration