Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
1.

To summarise the relationship between
degrees and radians

2.

To understand the term angular
displacement

3.

To def...
Angles can be measured in both degrees & radians :
Arc
length
θ
r

The angle θ in radians is defined as
the arc length / t...
Angular velocity, for circular motion, has
counterparts which can be compared with linear
speed s=Δx/Δt.
Period of time (Δ...
For a watch calculate the angular displacement in
radians of the tip of the minute hand in
1. One second
2. One minute
3. ...
Consider an object moving along the arc of a circle
from A to P at a constant linear speed for time Δt:
Arc length

Defini...
The period T of the rotational motion is the time
taken for one complete revolution (2π radians).
Substituting into : ω = ...
Considering the diagram below, we can see that
the linear distance travelled is the arc length
P
Arc length
r
θ
r

A

∴ Li...
A cyclist travels at a linear speed of 12 ms-1 on a
bike with wheels which have a radius of 40 cm.
The wheels rotate clock...
The frequency of rotation for the wheels
Circumference of the wheel is 2π r
= 2π x 0.40m = 2.5m
Time for one rotation, (th...
The angular velocity for the wheels
Using T = 2π / ω , rearranged for ω

ω = 2π / T
ω = 2π / 0.21
ω = 30 rads-1 Clockwise
The angle the wheel turns through in 0.10s in
i radians ii degrees
Using ω = Δθ / Δt

re-arranged for Δθ

Δθ = ω t
Δθ = 30...
Physics a2 unit4_05_circular_motion_01 phyiscs circular motion
Upcoming SlideShare
Loading in …5
×

Physics a2 unit4_05_circular_motion_01 phyiscs circular motion

255 views

Published on

Published in: Education
  • Be the first to comment

Physics a2 unit4_05_circular_motion_01 phyiscs circular motion

  1. 1. 1. To summarise the relationship between degrees and radians 2. To understand the term angular displacement 3. To define angular velocity 4. To connect angular velocity to the period and frequency of rotation 5. To connect angular velocity to linear speed
  2. 2. Angles can be measured in both degrees & radians : Arc length θ r The angle θ in radians is defined as the arc length / the radius For a whole circle, (360°) the arc length is the circumference, (2π r) ∴ 360° is 2π radians (or “rad”) Common values : 45° = π /4 radians 90° = π /2 radians 180° = π radians Note. In S.I. Units we use “rad” How many degrees is 1 radian?
  3. 3. Angular velocity, for circular motion, has counterparts which can be compared with linear speed s=Δx/Δt. Period of time (Δt) remains unchanged, but linear distance (Δx) is replaced with angular displacement Δθ measured in radians. Angular displacement Δθ r Δθ r Angular displacement is the number of radians moved
  4. 4. For a watch calculate the angular displacement in radians of the tip of the minute hand in 1. One second 2. One minute 3. One hour Each full rotation of the London eye takes 30 minutes. What is the angular displacement per second?
  5. 5. Consider an object moving along the arc of a circle from A to P at a constant linear speed for time Δt: Arc length Definition : The rate of change of angular displacement with time A “The angle, (in radians) an object rotates through per second” P r θ r ω = Δθ / Δt Where Δθ is the angle turned through in radians, (rad), yields units for ω of rads-1 This is all very comparable with linear speed, (or velocity) where we talk about distance/time
  6. 6. The period T of the rotational motion is the time taken for one complete revolution (2π radians). Substituting into : ω = Δθ / Δt ω = 2π / T ∴ T = 2π / ω From our earlier work on waves we know that the period (T) & frequency (f) are related T = 1/f ∴ f = ω / 2π
  7. 7. Considering the diagram below, we can see that the linear distance travelled is the arc length P Arc length r θ r A ∴ Linear speed (v) = arc length (AP) / Δt v = r Δθ / Δt Substituting... (ω = Δθ / Δt) v = ωr
  8. 8. A cyclist travels at a linear speed of 12 ms-1 on a bike with wheels which have a radius of 40 cm. The wheels rotate clockwise. Calculate: a. The frequency of rotation for the wheels b. The angular velocity for the wheels c. The angle the wheel turns through in 0.10 s in i. radians ii. degrees
  9. 9. The frequency of rotation for the wheels Circumference of the wheel is 2π r = 2π x 0.40m = 2.5m Time for one rotation, (the period) is found using s = Δd / Δt rearranged for Δt Δt = Δd / s = T = circumference / linear speed T = 2.5 / 12 = 0.21s f = 1 / T = 1 / 0.21 = 4.8Hz
  10. 10. The angular velocity for the wheels Using T = 2π / ω , rearranged for ω ω = 2π / T ω = 2π / 0.21 ω = 30 rads-1 Clockwise
  11. 11. The angle the wheel turns through in 0.10s in i radians ii degrees Using ω = Δθ / Δt re-arranged for Δθ Δθ = ω t Δθ = 30 x 0.10 Δθ = 3.0 rad = 3.0 x (360°/ 2π ) = 172° ≈ 1.7 x 102 °

×