Rotational Motion

1
Rotational Motion
2
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.

3
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
• Equation t F-l
• t Torque (Nm)
• F- Force perpendicular (N)
• l lever arm length (m)

4

• 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

5

• 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

6
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.

7
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?

8

• 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.

9
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.

10
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.