Rotational Dynamics: Torque

1. Rotational Dynamics: Torque Practice Problems Newton’s 2nd law involving rotations

2. Practice Problem #2 • A person exerts a force of 45.0 N on the end of a door 84.0 cm wide. What is the magnitude of the torque if the force is exerted: • Perpendicular to the door? • At a 60.0° angle to the face of the door?

3. Practice problem #3 • If the coefficient of static friction between tires and pavement is 0.75, calculate the minimum torque that must be applied to the 66 cm diameter tire of a 1080 kg automobile in order to “lay rubber” (make the wheels spin, slipping as the car accelerates). Assume each wheel supports an equal share of the weight.

4. Practice problem #4 • The bolts on the cylinder head of an engine require tightening to a torque of 80.0 m·N. If a wrench is 30.0 cm long, what force perpendicular to the wrench must the mechanic exert at its end?

5. Biceps’ torque • The biceps muscle exerts a vertical force on the lower arm. Assume that the muscle attaches to the arm 5.0 cm away from the elbow joint. • If the muscle exerts 700.0 N of force, what is the applied torque when the arm is as shown in the image above?

6. Net torque • The total sum of each torque acting on a body. • If both torques would/could cause a clockwise rotation or a counter-clockwise rotation, then the net torque is the sum of the magnitudes. • If both torques would/could cause a rotation in opposite directions, the net torque is the difference of the two. • Assign a + and a – direction to the clockwise and counter-clockwise directions (your choice…keep it consistent)

7. Static Equilibrium • Occurs when both the net torque and the net force are equal to zero. • No rotation and no linear acceleration will occur

8. Net Torque • Will cause an object to…do what? • Rotate with an angular acceleration that is proportional to the magnitude and in the direction of the net torque. • Newton’s 2nd Law…for rotational motion! • What are some factors that may affect the magnitude of the acceleration that the torque creates?

9. Moment of Inertia (I) • Determines how easily a mass can be rotated about a fixed axis • For a single particle (point mass) of mass m, rotating at a distance r about an axis, the moment of inertia is: • More than one mass? Add the moments of inertia together: • All specific equations will be provided 

10. Examples of moments of inertia: • Simple Pendulum—a single mass on the end of a string: • Dumbbell—2 masses (m) connected by a light rod (length = l):

11. Couples • A “Couple” in rotational mechanics refers to a system that is acted on by two applied forces. • By definition, a Couple is: • A pair of equal and opposite forces that do not act in the same straight line. • The forces in a couple may result in static equilibrium, but they may also result in an angular acceleration—but no linear acceleration. • i.e. the forces of your hands on a steering wheel; the weights of two people on opposite sides of a teeter-totter. • (see page 553 )

12. Torque as a “vector” • To determine the direction of Torque that does not depend on your viewpoint (i.e. clockwise and counter-clockwise depend on what side of the rotation you’re viewing it from), Use the right-hand rule: The direction of torque is perpendicular to the planeof the rotating body: