AP Physics

Mr. Jean

April 27th, 2012

The plan:

• Quest Assignment

• High Level Question Handout– AP Handouts PDF.– With Solutions

• Torque

• AP Sample Exam

High Level Questions:

• Here is a high level Physics exam which covers many of the same concepts you have in this course.

– It requires significant amount of application and understanding the concepts in class.

– Also, you have the solutions.. The solutions will help demonstrate how to approach these questions as well as how they are marked.

• I would peg this exam as “more difficult” when compared to what you would expect on May 14th.

Quest

• Quest Assignment #3– Due May 6th, 2012

Torque:

• Forces: – We’ve learned that forces change the velocity

of an object. – But what does it take to change the angular

velocity of a thing? – Well, forces are involved, but the force has to

be applied in a special way. We call this special applied force a torque.

• Torques change angular velocity. The symbol for torque is the Greek letter . Torque is given by this equation:

sinrF r is the distance to the center of spin from where the force is applied. This variable is often called the lever arm.

F sin be the force component that is perpendicular to the lever arm

Components of Torque:

r

F

F s in

sinrF

Torque Units:

• The unit for torque is going to be a newton meter(nm). Woohoo…

• This looks very similar to the unit for work, the joule, but it is quite different.

• So energy and work are in joules and torque is left in newton meters.

Example Question:

• 125 N is applied to a nut by a wrench. The length of the wrench is 0.300 m. What is the torque?

125 0.300 37.5Fr N m Nm

Example Question #2:

• A torque of 857 Nm is applied to flywheel that has a radius of 45.5 cm. What is the applied force?

1857 1880

0.455Fr F Nm N

r m

Example Question:

• You push on the door as shown in the drawing. What is the torque?

330 N

1.5 m 55.0

sinrF

330 1.5 sin55.0N m

410 Nm

Multiple Torques: • What happens if two or more torques act

on an object at the same time?

• Two forces are applied to the object. The object is free to rotate about the spin axis. Both cause a torque.

sp in ax is

F2

F1

r1

r2

• F1 causes a CCW (counter clockwise) rotation around the axis.

• F2 causes a CW (clockwise) rotation around the axis.

• If a torque causes a clockwise rotation, it is positive.

• If a torque causes a counter clockwise rotation, it is negative.

• The sum of the two torques would be:

1 2 2 2 1 1 = F r F r

Equilibrium and Torque:

• If an object is in angular equilibrium (sometimes called rotational equilibrium), then it is either at rest or else it is rotating with a constant angular:

• If object is in rotational equilibrium, the net torque about any axis is zero

= 0

• Static equilibrium exists when an object has no motion, either linear or angular. There are two conditions which must exist in order to have your good old static equilibrium:

• The net force must be zero and the net torque must be zero. F = 0 = 0

• This gives us some very powerful tools to solve static problems. We can analyze a system and look at the forces acting on it, and we can also look at the torques that act on it. We’ll be able to do some really cool stuff.

• For example:

• Two metal orbs are attached to a very lightweight rigid wire. They are suspended from a rigid point on the overhead as shown. The system does not move. Calculate the distance from the suspension line to the center of gravity on the right sphere.

1 .0 kg 4 .0 kg

45 .0 cm ?

Free Body Diagram (ish)

m g

F

1m g2

• Without using the torque equilibrium, we could not solve the problem. The sum of forces would simply tell us that the upward force would be equal to weight of the two balls.

• Using torque, however, allows us to solve the problem.

• All we have to do is add up d’ torques:

m g r1 m g r2

r1 r2

12

Solution:

1 11 2 1 1 2 2 2 2 1 1 2

2

0 0m gr

m gr m gr m gr m gr rm g

2

1.0 0.450.11 11

4.0

kg mr m or cm

kg

m g r1 m g r2

r1 r2

12

• Next class: – The classic Teeter-totter balance beam– Fabulous Ladder Problems (typical AP stuff)– Support hanging off the side of a building.

– http://www.brightstorm.com/science/physics/circular-motion-and-rotational-mechanics/torque/

AP 2005:

• Physics AP Exam B.