Rotational Motion

1
Rotational Motion

• Chapters
• 10, 11, 12

2
Rotation vs Revolution

• An axis is the straight line around which
  rotation takes place.
• When an object turns about an internal axis, the
  motion is called rotation, or spin.
• When an object turns about an external axis, the
  motion is called revolution.

3
Rotation vs. Revolution

• The Ferris wheel turns about an axis.
• The Ferris wheel rotates, while the riders
  revolve about its axis.
• Earth undergoes both types of rotational motion.

4
Rotational Speed

• The turntable rotates around its axis while a
  ladybug sitting at its edge revolves around the
  same axis.

Which part of the turntable moves fasterthe
outer part where the ladybug sits or a part near
the orange center?
Answer It depends on whether you are talking
about linear speed or rotational speed.
5
Rotational Speed

• Linear speed is the distance traveled per unit of
  time.
• The linear speed is greater on the outer edge of
  a rotating object than it is closer to the axis
  (travels a greater distance in one rotation than
  a point near the center).
• The speed of something moving along a circular
  path can be called tangential speed because the
  direction of motion is always tangent to the
  circle.

6
Rotational Speed

• Rotational speed (sometimes called angular speed)
  is the number of rotations per unit of time.
• All parts of the rigid turntable rotate about the
  axis in the same amount of time.
• All parts have the same rate of rotation, or the
  same number of rotations per unit of time. It is
  common to express rotational speed in revolutions
  per minute (RPM).

7
Rotational Speed

• All parts of the turntable rotate at the same
  rotational speed.
• A point farther away from the center travels a
  longer path in the same time and therefore has a
  greater tangential speed.
• A ladybug sitting twice as far from the center
  moves twice as fast.

8
Rotational Speed

• At the axis of the rotating platform, you have no
  tangential speed, but you do have rotational
  speed. You rotate in one place.
• As you move away from the center, your tangential
  speed increases while your rotational speed stays
  the same.
• Move out twice as far from the center, and you
  have twice the tangential speed.

9
Rotational Speed

• think!
• Q. At an amusement park, you and a friend sit on
  a large rotating disk. You sit at the edge and
  have a rotational speed of 4 RPM and a linear
  speed of 6 m/s. Your friend sits halfway to the
  center. What is her rotational speed? What is her
  linear speed?

10
Rotational Speed

• Why does a tapered cup roll in a curved path?

11
Rotational Speed

• Why does this shape remain on the track?

12
Rotational Speed

• Why is the tapered shape (exaggerated) of
  railroad train wheels essential on the curves of
  railroad tracks?

13
Rotational Speed

• think!
• Train wheels ride on a pair of tracks. For
  straight-line motion, both tracks are the same
  length. But which track is longer for a curve,
  the one on the outside or the one on the inside
  of the curve?

14
Centripetal Force

• Velocity (a vector) involves both speed and
  direction.
• When an object moves in a circle, even at
  constant speed, the object still undergoes
  acceleration because its direction is changing.
• This change in direction is due to a net force
  (otherwise the object would continue to go in a
  straight line).
• Any object moving in a circle undergoes an
  acceleration that is directed to the center of
  the circlea centripetal acceleration.

15
Centripetal Force

• Centripetal means toward the center.
• The force directed toward a fixed center that
  causes an object to follow a circular path is
  called a centripetal force.

16
Centripetal Force

• Centripetal force holds a car in a curved path.
• For the car to go around a curve, there must be
  sufficient friction to provide the required
  centripetal force.
• If the force of friction is not great enough,
  skidding occurs.

17
Centripetal Force

• Calculating Centripetal Force

Centripetal force, Fc, is measured in newtons
when m is expressed in kilograms, v in
meters/second, and r in meters.
18
Centripetal vs. Centrifugal Force

• Sometimes an outward force is also attributed to
  circular motion.
• This apparent outward force on a rotating or
  revolving body is called centrifugal force.
  Centrifugal means center-fleeing, or away from
  the center.
• This force does not exist!

19
Centripetal vs. Centrifugal Force

• In the case of the whirling can, it is a common
  misconception to state that a centrifugal force
  pulls outward on the can.
• In fact, when the string breaks the can goes off
  in a tangential straight-line path because no
  force acts on it.
• So when you swing a tin can in a circular path,
  there is no force pulling the can outward (no
  centrifugal force).
• Only the force from the string acts on the can to
  pull the can inward.

20
Chapter 11 Rotational Equilibrium

• This chapter is about the factors that affect
  rotational equilibrium.

21
Torque

• Every time you open a door, turn on a water
  faucet, or tighten a nut with a wrench, you exert
  a turning force.
• Torque is produced by this turning force and
  tends to produce rotational acceleration.
• Torque is different from force.
• Forces tend to make things accelerate.
• Torques produce rotation.

22
Torque

• A torque produces rotation.

23
Torque

• The distance from the turning axis to the point
  of contact is called the lever arm.
• If the force is not at right angle to the lever
  arm, then only the perpendicular component of the
  force will contribute to the torque.

24
Torque

• Although the magnitudes of the applied forces are
  the same in each case, the torques are different.

25
Torque

• 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
  handle as shown?

26
Balanced Torques

• Children can balance a seesaw even when their
  weights are not equal.

27
Balanced Torques

• What is the weight of the block hung at the 10-cm
  mark?

28
Center of Mass

• The center of mass, is where all the mass of an
  object can be considered to be concentrated.
• For a symmetrical object, such as a baseball, the
  center of mass is at the geometric center of the
  object.
• For an irregularly shaped object, such as a
  hammer, the center of mass is toward the heavier
  end.

29
Center of Mass

• The center of mass of the toy is below its
  geometric center.

30
Center of Mass

• The center of mass of the rotating wrench follows
  a straight-line path as it slides across a smooth
  surface.

31
Center of Mass vs Center of Gravity

• Center of mass is often called center of gravity,
  the average position of all the particles of
  weight that make up an object.
• For almost all objects on and near Earth, these
  terms are interchangeable.
• There can be a small difference between center of
  gravity and center of mass when an object is
  large enough for gravity to vary from one part to
  another.
• For example)
• The center of gravity of the Sears Tower in
  Chicago is about 1 mm below its center of mass
  because the lower stories are pulled a little
  more strongly by Earths gravity than the upper
  stories.

32
Center of Gravity

• The CG is the balance point.
• Supporting that single point supports the whole
  object.

33
Center of Gravity

• There is no material at the CG of these objects.

34
Torque and CG

• The block topples when the CG extends beyond its
  support base.

35
Torque and CG

• The Rule for Toppling
• If the CG extends outside the area of support,
  an unbalanced torque exists, and the object will
  topple.

36
Torque and CG

• This Londoner double-decker bus is undergoing a
  tilt test.
• So much of the weight of the vehicle is in the
  lower part that the bus can be tilted beyond 28
  without toppling.

37
Torque and CG

• The Leaning Tower of Pisa does not topple over
  because its CG lies above its base.

38
Center of Gravity and People

• When you stand, your CG is somewhere above the
  area bounded by your feet.

39
Center of Gravity and People

• You can lean over and touch your toes without
  toppling only if your CG is above the area
  bounded by your feet.

40
Center of Gravity and People

• Think
• When you carry a heavy loadsuch as a pail of
  waterwith one arm, why do you tend to hold your
  free arm out horizontally?