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:Torque: the perpendicular force times the perpendicular force times the lever arm lengththe lever arm length Torque produce rotations The force must be perpendicular to the lever

arm Ex: turning a door knob; bending your arm

Equation: ττ = F = F┴┴ll• 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:Fulcrum: the pivot point of a lever 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 UnderstandingCheck Your Understanding

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