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### Torque & Equilibrium

It’s gravy n I got it all smothered, like make-up I got it all covered

Its all kinda confusing

Review

- Rotational Kinetic Energy Krot = ½ I w2
- Rotational Inertia I = S miri2
- Energy Still Conserved!

Today

- Torque

Working without guidance is the hardest part for me! It seems like I need someone

There to tell me if I’m doing it right or wrong!!

05

50 cm

2kg

Torque- A meter stick is suspended at the center. If a 1 kg weight is placed at x=0. Where do you need to place a 2 kg weight to balance it?

A) x = 25 B) x = 50 C) x = 75 D) x = 100

E) 1 kg can’t balance a 2 kg weight.

understanding when things are negative

1 kg

just keeping everything straight in my head and not mixing

things up

Torque

Torque was a strange concept to me

- Rotational effect of force. Tells how effective force is at twisting or rotating an object or at changing the rate of rotation.
- t = +- r Fperpendicular = r F sin q
- Units N m
- Sign: CCW rotation is positive

torque and angels

Torque is still a little confusing… but nothing an example couldn’t fix

30

F=89 N

Torque Example and ACTA person raises one leg to an angle of 30 degrees. An ankle weight (89 N) attached a distance of 0.84 m from her hip. What is the torque due to this weight?

1) Draw Diagram

2) t = F r sin q

= F r sin(90 – 30)

If she raises her leg higher, the torque due to the weight will

A) Increase

B) Same

C) Decrease

= 90 - 30

In degrees

= 65 N m

x

Equilibrium Acts- A rod is lying on a table and has two equal but opposite forces acting on it at different points. What is the net force on the rod?

A) Up B) Down C) Zero

- Will the rod move? A) Yes B) No

Y direction: S Fy = may

+F – F = 0

F

Yes, it rotates!

F

50 cm

19.6 N

9.8 N

Equilibrium- Conditions for Equilibrium
- S F = 0 Translational EQ (Center of Mass)
- St = 0 Rotational EQ (True for any axis!)
- Choose axis of rotation wisely!
- A meter stick is suspended at the center. If a 1 kg weight is placed at x=0. Where do you need to place a 2 kg weight to balance it?

A) x = 25 B) x=50 C) x=75 D) x=100

E) 1 kg can’t balance a 2 kg weight.

putting the equations together

S t = 0

9.8 (0.5) – (19.6)d = 0

d = 25

pivot

d

W=mg

Static Equilibrium and Center of Mass- Gravitational Force Weight = mg
- Acts as force at center of mass
- Torque about pivot due to gravity t = mgd
- Object not in static equilibrium

It’s all kinda confusing

Center of mass

pivot

d

Center of mass

W=mg

Torque about pivot = 0

Torque about pivot 0

Static EquilibriumNot in equilibrium

Equilibrium

A method to find center of mass of an irregular object

31

Preflight

The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight?

1. The person on the left is supporting the greatest weight

2. The person on the right is supporting the greatest weight

3. They are supporting the same weight

“i feel like the person in the back would be doing all the work”

“The person on the left is closer to the center. This equates to a smaller r value and thus a larger F value in the torque equation.”

FL

FR

L

L/2

mg

PreflightThe picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight?

1. The person on the left is supporting the greatest weight

2. The person on the right is supporting the greatest weight

3. They are supporting the same weight

Look at torque about center:

FR L – FL L/2 = 0

FR= ½ FL

FB

1 meter

0.5meter

mg

Mg

Homework 8 HintsA 75 kg painter stands at the center of a 50 kg, 3 meter plank. The supports are 1 meter in from each edge. Calculate the force on support A.

1 meter

1 meter

B

A

1) Draw FBD

2) SF = 0

3) Choose pivot

4) St = 0

FA + FB – mg – Mg = 0

-FA (1) sin(90)+ FB (0) sin(90) + mg (0.5)sin(90) + Mg(0.5) sin(90) = 0

FA = 0.5 mg + 0.5 Mg = 612.5 Newtons

Homework 8 Hints

If the painter moves to the right, the force exerted by support A

A) Increases B) Unchanged C) Decreases

1 meter

1 meter

B

A

x

0.5meter

Mg

mg

Homework 8 HintsHow far to the right of support B can the painter stand before the plank tips?

1 meter

1 meter

B

A

Just before board tips, force from A becomes zero

1) Draw Force Diagram

2) SF = 0

3) Choose pivot

4) St = 0

FB – mg – Mg = 0

FB (0) sin(90) + mg (0.5)sin(90) – Mg(x) sin(90) = 0

0.5 m = x M

F2

mg

Equilibrium ExampleA 50 kg diver stands at the end of a 4.6 m diving board. Neglecting the weight of the board, what is the force on the pivot 1.2 meters from the end?

1) Draw Force Diagram

2) Choose Axis of rotation

3) St = 0 Rotational EQ

F1 (1.2) – mg (4.6) = 0

F1 = 4.6 (50 *9.8) / 1.2

F1 = 1880 N

4) S F = 0 Translational EQ

F1 – F2 – mg = 0

F2 = F1 – mg = 1390 N

Summary

- Torque = Force that causes rotation
- t = F r sin q
- Work done by torque W = t q
- Equilibrium
- S F = 0
- S t = 0
- Can choose any axis.

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