Rotational Motion

Difference between torque and force If you want to make an object move, apply a force If you want to make an object rotate, apply a torque. Forces produce accelerations. Torques produce rotations.

Torque Torque: the perpendicular force times the lever arm length  Torque produce rotations  The force must be perpendicular to the lever arm  Ex: turning a door knob; bending your arm τ = F ┴ l  Equation: τ = F ┴ l τ = Torque (N*m) F ┴ = Force perpendicular (N) l = lever arm length (m)

The lever arm length is distance from the fulcrum to the area where the force is perpendicularly applied. Fulcrum: the pivot point of a lever  Where rotation begins  Ex: hinge of a door, center of a seesaw, your knee or elbow

Torque and lever arm length are directly proportional.  2x lever arm length = 2 x Torque  ½ lever arm length = ½ Torque  3x lever arm length = 3x Torque  1/3 lever arm length = 1/3 Torque Torque and force are directly proportional  2x force = 2 x Torque  ½ force = ½ Torque  3x force = 3x Torque  1/3 force = 1/3 Torque

One way to produce more torque Although the magnitudes of the applied forces are the same, the torques are different. Only the component of forces perpendicular to the lever arm contributes to the force.

Check Your Understanding If you cannot exert enough torque to turn a stubborn bolt, would more torque be produced if you fastened a length of rope to the wrench as shown?

No, because the lever arm (the arm of the wrench) is the same. If you wanted to increase the lever arm, you would need to use a longer wrench.

Balanced Torques Weight does not produce rotation, torque does. Consider a heavy boy and a slim boy on a seesaw. In order to balance the seesaw, the heavy boy must sit closer to the middle than the slim boy. In this way, the counter clock wise torque produced by the slim boy will equal the clock wise torque produced by the heavy boy.

Check Your Understanding Two children are on a seesaw. Child A is twice as heavy as Child B. Which one will sit closer towards the center to make them balanced? Child A because a larger mass must have a smaller lever arm length to balance the smaller mass with the larger lever arm length of Child B.