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Circular motion.

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Presentation on theme: "Circular motion."— Presentation transcript:

1 Circular motion

2 Measuring Circular Motion (Method 1)
1 complete rotation = 1 revolution Measure rotational motion by counting the number of rotations Most common unit of measurement = revolution (abbreviated rev)

3 Measuring Circular Motion (Method 2)
360° Can also measure using degrees 1 rotation = 1 revolution = 360°

4 Measuring Circular Motion (Method 3)
Θ=s/r Radian (rad): angle with vertex at center of circle whose sides cut off an arc on circle equal to its radius Radius = r Length of arc = s angle = 1 radian Unitless dimension – use rad to avoid confusion

5 Converting between different measurement
By definition: 1 rev = 360° = 2π rad Convert 10π rad to revolutions

6 Converting from Degree to Rad
θrad=(π/180)θdegrees Convert 75 degrees to radians

7 Angular Displacement Distance through which any point on rotating body moves (angular distance instead of linear distance) Example: when a wheel makes one complete rotation, it’s angular displacement has been 1 rev, 2π rad, or 360°

8 Angular Velocity Similar to linear velocity, except instead of linear displacement, use angular displacement Angular velocity = rev/time OR ω = angular displacement (θ)/time (t) Units = rad/s or rev/min θ t ω =

9 Example A motorcycle wheel turns 7200 times while being ridden for 10 min. What is the angular velocity in rev/min?

10 Linear Velocity The linear speed on any point on rotating circle = v = ωr v = linear velocity ω = angular velocity r = radius Can measure using stroboscope or strobe light

11 Example: Linear Velocity
A wheel of 1.00 m radius turns at 1000 rpm. Find the linear speed of a point on the rim of the wheel.

12 α = Δω t Angular Acceleration α = angular acceleration
Angular acceleration = rate of change of angular velocity α = angular acceleration Δω = change in angular velocity t = time Δω t α =

13 Equations: Linear vs. Rotational Motion
Linear Motion Equations Rotational Motion Equations s = vavgt θ = ωavgt s = vit + ½aavgt2 θ = ωit + ½αavg t2 vavg = (vf + vi)/t ωavg = (ωf + ωi)/t aavg = (vf – vi)/t αavg = (ωf – ωi)/t 2aavgs = vf2 – vi2 2αavgθ = ωf2 – ωi2

14 Sample Calculations To calculate various components of angular motion, click on the link listed below: ics/hbase/rotq.html


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