Rotational Motion

1
Rotational Motion
2
Rotational v. Linear Speed

• Linear speed is distance per unit of time. v
  d/t
• Tangential speed is distance per unit of time but
  along a circular path. v 2pr/t
• Linear and tangential basically mean the same
  thing.
• Tangential speed is directly proportional to the
  distance from the axis of rotation.

3
Rotational Speed

• Also called angular speed
• Number of rotations per unit of time (for example
  33 RPMs 33 rotations per minute)
• Rotational speed does NOT depend on distance from
  the axis of rotation.

4
Forces involved during rotational motion

• Centripetal force center-seeking force
• When you spin a bucket of water, a centripetal
  force is applied by your hand on the bucket and
  by the bottom of the bucket on the water
• Centrifugal force center-fleeing force
• The centrifugal force in the above example is the
  inertia of the bucket of water wanting to fly
  away from you and the inertia of the water
  pressing against the bottom of the bucket

5
Torque

• When a force is applied in a motion that is
  perpendicular to the distance, a torque is
  produce and a rotational motion is created
• The pivot point about which rotation occurs is
  called the fulcrum
• The distance between the the point where the
  force is applied and the fulcrum is called the
  lever arm
• Torque is considered to be either clockwise or
  counterclockwise, as when using a wrench to
  loosen a nut

6
Calculating torque

• Torque is calculated by multiplying the
  application force by the lever arm
• Torque is measured in Newton-meters (in the world
  of automechanics it is measured in foot-lbs)

7
Visualizing Torque

• When a counterclockwise torque and a clockwise
  torque on the same system are equal, you have a
  situation called dynamic equilibrium (i.e.-having
  two kids sit on a seesaw and both sides are equal
  in torque so no motion/rotation occurs)
• Answer this Two kids sit on a seesaw and its
  balanced, the kid on the left side leans forward.
  Does the seesaw move? If so which way AND why
  in that direction?

8

• Answer to seesaw question In the beginning the
  torques were equal, but when the kid on the left
  leaned forward, the lever arm distance was
  reduced and therefore the torque was reduced. So
  the right side now has more torque and will
  sink producing a clockwise torque. There is
  now a net torque in the clockwise direction.
  Torque is a vector quantity.

9
Visualizing torque again

• Using the idea of torque, explain why door
  knobs are placed at the outer edge of a door
  rather than in the center of a door?

10

• Having the knob at the edge, the farthest away
  from the fulcrum, reduces the effort force needed
  to open the door. The torque is the same no
  matter where the door knob is located, but having
  the knob at the edge increases the lever arm
  distance from the pivot point (point of rotation).