1. Torque

2. How do you make an object start to rotate?
Pick an object in the room and list all the ways you can think of to make it start rotating.

3. Torque
Let’s say we want to spin a can on the table. A force is required.
One way to start rotation is to wind a string around outer edge of can and then pull.
Where is the force acting?
In which direction is the force acting?

4. Torque
Force acting on outside of can. Where string leaves the can, pulling tangent.

5. Torque Where you apply the force is important.
Think of trying to open a heavy door- if you push right next to the hinges (axis of rotation) it is very hard to move. If you push far from the hinges it is easier to move.
Distance from axis of rotation =
lever arm or moment arm

6. Torque Which string will open the door the easiest?
In which direction do you need to pull the string to make the door open easiest?

7. Torque

8. Torque  =rFsin  tau = torque (mN) If force is perpendicular,  =rF
If force is not perpendicular, need to find the perpendicular component of F
 =rFsin
Where = angle btwn F and r

9. Torque example (perpendicular)
Ned tightens a bolt in his car engine by exerting 12N of force on his wrench at a distance of 0.40m from the fulcrum. How much torque must he produce to turn the bolt? (force is applied perpendicular to rotation)
Torque=  =rF=(12N)(0.4m)=4.8mN

10. Torque- Example glencoe p. 202
A bolt on a car engine needs to be tightened with a torque of 35 mN. You use a 25cm long wrench and pull on the end of the wrench at an angle of 60.0 from perpendicular. How long is the lever arm and how much force do you have to exert?
Sketch the problem before solving

11. More than one Torque
When 1 torque acting, angular acceleration  is proportional to net torque
If forces acting to rotate object in same direction net torque=sum of torques
If forces acting to rotate object in opposite directions net torque=difference of torques
Counterclockwise +
Clockwise -

12. Multiple Torque experiment
Balance a meter stick on a pivot.
Now balance the meter stick by adding 2 different masses- on on each side of the fulcrum.
Derive an equation to show this equilibrium.

13. Torque and football
If you kick the ball at the center of mass it will not spin
If you kick the ball above or below the center of mass it will spin

14. Inertia Remember our friend, Newton? F=ma In circular motion:
torque takes the place of force
Angular acceleration takes the place of acceleration

15. Rotational Inertia=LAZINESS
Moment of inertia for a point object
I = Resistance to rotation
I=mr2 = I 
I plays the same role for rotational motion as mass does for translational motion
I depends on distribution of mass with respect to axis of rotation
When mass is concentrated close to axis of rotation, I is lower so easier to start and stop rotation

16. Rotational Inertia Unlike translational motion, distribution of mass is important in rotational motion.

17. Changing rotational inertia
When you change your rotational inertia you can drastically change your velocity
So what about conservation of momentum?

18. Angular momentum
Momentum is conserved when no outside forces are acting
In rotation- this means if no outside torques are acting
A spinning ice skater pulls in her arms (decreasing her radius of spin) and spins faster yet her momentum is conserved

19. Angular momentum Angular momentum=L
L= vector cross product of radius times momentum
L=r x ρ
Right hand rule
point fingers out the r and curl them in direction of ρ: your thumb will point in direction of L
Unit is kgm2/s
Vector cross product: r, ρ, and L are mutually perpendicular to each other

20. The Ice Skater Revisited
The ice skater’s angular momentum is conserved when she spins
Arms out= increased radius so decreased momentum (since mass is unchanged this means decreased velocity)
Using right hand rule, which direction is angular momentum?

21. Angular momentum: football, bullets
When you throw a football or shoot a bullet you put a spin on it
Use right hand rule to find direction of L for a right-handed quarterback
Why does this spin help?
Large ships often have a large, heavy spinning wheel to resist torque from waves

22. Examples… Hickory Dickory Dock…
A 20.0g mouse ran up a clock and took turns riding the second hand (0.20m), minute hand (0.20m), and the hour hand (0.10m). What was the angular momentum of the mouse on each of the 3 hands and in what direction?
Try as a group.