Angular Displacement and Speed

1
Rotational Motion

• Angular Displacement and Speed
• HMH Physics Chapter 7 pages 224-269
• Section 1 pages 226-231

2

1. Convert angle measurements between degrees and
   radians.
2. Explain the right hand rule and vector direction
   of circular motion.
3. Calculate Arc length traveled during circular
   motion.
4. Calculate Angular Speed.

3
Rotational Quantities

• Rotational motion
• the motion when an object spins
• Circular motion is described in terms of the angle

4

• T the angle
• s the arc length in meters
• the distance measured along the circumference of
  a circle
• r the length of the radius in meters
• (distance of the object from the axis of
  rotation)

s
T
r
5

• Angles are often measured in radians in science
• An angle in radians is the ratio of the arc
  length to the radius
• s
• T ---
• r
• T has no units, but we use the abbreviation rad
  when the angle is measured in radians

6

• One revolution in a circle is 360, which is
  equal to 2? rad
• ? 2? rad
• 360o 2? rad
• 1 turn or revolution 2? rad

7

• You can use this formula to convert an angle in
  degrees to an angle in radians (or some
  calculators have a function to convert for you)
• ?
• T (rad) --- T (deg)
• 180

8

• Angular displacement describes how much an object
  has rotated
• It is the change in the arc length, ?s, divided
  by the distance of the object from the axis of
  rotation, r
• ?s
• ?T ---
• r

9

• When an object rotates counterclockwise, the arc
  length, s, and angular displacement, ?T, are
  considered positive
• When an object rotates clockwise, the arc length,
  s, and angular displacement, ?T, are considered
  negative

-
10

• While riding a carousel that is rotating
  clockwise, a child travels through an arc length
  of 11.5 m. If the childs angular displacement
  is 165, what is the radius of the carousel?

11

• Angular speed describes rate of revolution
• It is the ratio of the angular displacement to
  the time interval
• ?T
• ?avg ---- units rad/s
• ?t
• Similar to the linear equation for velocity
• ?x
• Vavg ---
• ?t

12

• A child at an ice cream parlor spins on a stool.
  The child turns counterclockwise with an average
  angular speed of 4.0 rad/s. In what time
  interval will the childs feet have an angular
  displacement of 8.0? rad?