Peoples Physics Concepts

http://www.ck12.org Chapter 5. Centripetal Forces

5.2 Angular Speed

• Compare and contrast angular speed (ω) and tangential speed (v).


• Calculate both angular speed and tangential speed.

Students will learn the difference between angular speed (ω) and tangential speed (v) and how to calculate both.

Key Equations

ω= 2 π/T= 2 πf; Relationship between period and angular frequency.

ω=∆θ∆t =∆rts=vr

v=ωr

Guidance

• When something rotates in a circle, it moves through aposition angleθthat runs from 0 to 2πradians and
  starts over again at 0. The physical distance it moves is called thepath length. If the radius of the circle
  is larger, the path length traveled is longer. According to the arc length formulas=rθ, the path length∆s
  traveled by something at radiusrthrough an angleθis:

∆s=r∆θ[1]

• Just like the linear velocity is the rate of change of distance, angular velocity, usually calledω, is the rate of
  change ofθ. The direction of angular velocity is either clockwise or counterclockwise. Analogously, the rate
  of change ofωis the angular accelerationα.


• For an object moving in a circle, the objects tangential speed is directly proportional to the distance it is from
  the rotation axis. the tangential speed (as shown in the key equations) equals this distance multiplied by the
  angular speed (in radians/sec).

Example 1

Question: A Merry Go Round is rotating once every 4 seconds. If you are on a horse that is 15 m from the rotation
axis, how fast are you moving (i.e. what is your tangential speed)?

Answer:

v=rω

Now we need to convert the angular speed to units of radians per second.

ω=^14 ((
rotations(((
second ∗

2 π

1

radians



rotation=π^2 radianssecond

v= 15 m×π 2 =^152 π≈ 23. 6 radianssecond