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

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

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.

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.

Torque has its sign torque τ = r X F

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

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

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

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

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.

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.

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

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

Applying a torque Calculate the torque

Applying a torque Calculate the torque

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

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

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

Torque and angular acceleration for a rigid body Calculate angular accelaration

Torque and angular acceleration for a rigid body Calculate angular acceleration