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CIRCULAR MOTION 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) MEASURING CIRCULAR MOTION (METHOD 2) 360° Can also measure using degrees 1 rotation = 1 revolution = 360° 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 CONVERTING BETWEEN DIFFERENT MEASUREMENT By definition: 1 rev = 360° = 2π rad Convert 10π rad to revolutions CONVERTING FROM DEGREE TO RAD θrad=(π/180)θdegrees Convert 75 degrees to radians 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° 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 ω= θ t EXAMPLE A motorcycle wheel turns 7200 times while being ridden for 10 min. What is the angular velocity in rev/min? 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 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. ANGULAR ACCELERATION Angular acceleration = rate of change of angular velocity α= Δω t α = angular acceleration Δω = change in angular velocity t = time EQUATIONS: LINEAR VS. ROTATIONAL MOTION Linear Motion Equations s = vavgt Rotational Motion Equations 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 SAMPLE CALCULATIONS To calculate various components of angular motion, click on the link listed below: http://canario.iqm.unicamp.br/MATDID/HyperPhys ics/hbase/rotq.html