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$\bullet$ A square metal plate 0.180 $\mathrm{m}$ on each side is pivoted about an axis through point $O$ at its center and perpendicular to the plate. (See Figure $10.45 .$ Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are $F_{1}=18.0 \mathrm{N}, F_{2}=26.0 \mathrm{N},$ and $F_{3}=14.0 \mathrm{N}$ . The plate and all forces are in the plane of the page.

2.5 $\mathrm{N} . \mathrm{m}$ Counterclockwise.

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

McMaster University

Lectures

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Hello. We are asked in problem number five to find the net on this rotating middle square plate. Played itself is rotating about point. Oh, right here in the center. There are three forces acting on this plate. Um, this force here is 26 news. This war's is 18 new moons, and this force here at an angle of 45 degrees is 14 news. So again, um, find network, we would be looking to some all the forces times they're perpendicular lever arms there. Three forces, they provide three different torques. Now, looking at each force, we want to kind of take a look at which one of these would provide positive torque versus which one would be negative. Tour. Positive torque is causing this object to rotate in a counterclockwise direction. That would be this 26 Newton force would cause count are a counterclockwise rotation. Where is this? So well in this 14 torque as well. Also, be positive. And this 18 would cause a clockwise rotation affords a negative torque. They're looking at our 32 works. We have forced times, liver arm. I meet this. It would be the perpendicular distance to divorce, which would be this. This square is a square plate that is 18 meters per side. So this distance here is 0.9 meters. The 18 Newton is a negative. Will provide a negative torque. Also with a lever arm of 180.9 It's this perpendicular distance here to the force and the perpendicular distance. Year to the force is actually this distance here. You remember that If this side here, this you look, it is a right triangle, both of these as 0.9 the hype hotness of that right triangle would be point 09 Britt to sew that for our final torque. Here, it would be the 14 times point No. Nine square root of two something. Those talks up, you would get a that torque of 2.5 meters positive, which means it actually provides a counterclockwise torque. Thank you for learning with me today.

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