1. Physics 7C lecture 12 Torque Thursday November 7, 8:00 AM – 9:20 AM
Engineering Hall 1200

2. Loosen a bolt
Which of the three equal-magnitude forces in the figure is most likely to loosen the bolt?

3. Loosen a bolt
Which of the three equal-magnitude forces in the figure is most likely to loosen the bolt?
torque τ is proportional to both force and distance.

4. Torque has its sign
The line of action of a force is the line along which the force vector lies.
The lever arm (or moment arm) for a force is the perpendicular distance from O to the line of action of the force (see figure).
The torque of a force with respect to O is the product of the force and its lever arm.

5. Torque has its sign
torque τ = r X F

6. The four forces shown all have the same magnitude: F1 = F2 = F3 = F4.
Q10.1 F1 F3
The four forces shown all have the same magnitude: F1 = F2 = F3 = F4.
Which force produces the greatest torque about the point O (marked by the blue dot)? O F2 F4
A. F1
B. F2
C. F3
D. F4
E. not enough information given to decide
Answer: A

7. A10.1 F1 F3
The four forces shown all have the same magnitude: F1 = F2 = F3 = F4.
Which force produces the greatest torque about the point O (marked by the blue dot)? O F2 F4
A. F1
B. F2
C. F3
D. F4
E. not enough information given to decide

8. Calculate torque
torque τ = r X F
F = Fx i + Fy j
r = x i + y j

9. acts on an object at a point
Q10.4
A force
acts on an object at a point
located at the position
What is the torque that this force applies about the origin?
A. zero B. C. D. E.
Answer: D

10. A10.4
A force
acts on an object at a point
located at the position
What is the torque that this force applies about the origin?
A. zero B. C. D. E.

11. Torque as a vector
Torque can be expressed as a vector using the vector product.
how to find the direction of torque using a right hand rule.

12. Q10.2 F1 F3
Which of the four forces shown here produces a torque about O that is directed out of the plane of the drawing? O F2 F4
A. F1
B. F2
C. F3
D. F4
E. more than one of these
Answer: D

13. A10.2 F1 F3
Which of the four forces shown here produces a torque about O that is directed out of the plane of the drawing? O F2 F4
A. F1
B. F2
C. F3
D. F4
E. more than one of these

14. Applying a torque
Calculate the torque

15. Applying a torque
Calculate the torque

16. Q10.3
A plumber pushes straight down on the end of a long wrench as shown. What is the magnitude of the torque he applies about the pipe at lower right?
A. (0.80 m)(900 N)sin 19°
B. (0.80 m)(900 N)cos 19°
C. (0.80 m)(900 N)tan 19°
D. none of the above
Answer: B

17. A10.3
A plumber pushes straight down on the end of a long wrench as shown. What is the magnitude of the torque he applies about the pipe at lower right?
A. (0.80 m)(900 N)sin 19°
B. (0.80 m)(900 N)cos 19°
C. (0.80 m)(900 N)tan 19°
D. none of the above

18. Torque and angular acceleration for a rigid body
The rotational analog of Newton’s second law for a rigid body is z =Iz.

19. Torque and angular acceleration for a rigid body
Calculate angular accelaration

20. Torque and angular acceleration for a rigid body
Calculate angular acceleration