For the first day of our lab, we studied the concept of “Torque”.

In the real world, forces are often not concurrent. They act upon different points on an object. In the figure, for example, two forces are pulling on different points of an object. Two questions can be asked:

- In which direction will the object be accelerated?
- Will the object rotate?

If the two forces were both applied at point A, the resultant would be the force vector shown, FR. In fact, FR points in the direction in which the object will be accelerated. (This idea will be investigated further in later experiments.)What about question 2? Will the object rotate? In this experiment we will begin to investigate the types of forces that cause rotation in physical bodies.

- First, find the mass of two of the protractors and record the masses.

-Protractor 1: 10.35g

-Protractor 2: 10.35g

2. Loosen the thumbscrews on the two protractors and slide one onto each of the beam. Tie a mass hanger to the thread on the angle indicator of each protractor.

**Procedure: Equal Distance, Equal Mass**

- Measure d1 and d2, the distances from the pivot to the center of each protractor.

-d1= 119mm

-d2= 120mm

2. Add a 50-gram mass to each mass hanger.

-> Is the beam still balanced? Yes!

3. Add an additional 20-gram to one of the mass hangers.

-> Can you restore the balance of the beam by repositioning the other protractor and mass hanger? Yes! You have to move the M2 from 120 to 93.

**Procedure #2: Unequal Distance, Unequal Mass**

- At the first balanced position, measure the total mass, M1 and M2, on each side of the pivot (protractor, mass hanger, added masses) and record the masses in the data table.

- Measure the distances, d1 and d2, between the centers of the protractors and the pivot and record the values in the data table.

=> d1= 85, d2=118.5

- Take measurements for five more different values of M2 and record your results in the data table. Be sure to include the units of your measurements.

- If there is time, vary M1 and repeat the procedure.

**Calculations**

-calculate: gravitational force produced by the total mass on each side of the beam, torques on each side of the beam,

**We have found out that for this experiment the torque, t, is F d(where Fg=mg) since the distance and the direction of the force are at right angles.

(Data Table) *Due to lack of time, we only went through two trials.

**Questions**

- From your results, what mathematical relationship must there be between t1 and t2 in order for the beam to be balanced?

Answer: t1+t2

- What torque is exerted on the balance beam by the upward pull of the pivot point?

Answer: 0 because there is no lever arm.

- What relationship must there be between t1, t2, and t3 in order for the beam to be balanced when there are three protractors and mass hangers?

Answer: t1=t2+t3 => t1+t2+t3=0.