chapter 8 rotational kinematics. radians angular displacement angle through which something is...
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Angular DisplacementAngle through which something is
rotated Counterclockwise => positive(+)
Units => radians
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θ =Arc length
Radius=s
r
Angular SpeedRate of Rotation
Counterclockwise => positive(+) Clockwise => negative(-)
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ωavg=ΔθΔt
Units => radians/secondAlso rev/min or rpm
Angular Acceleration
Units => radians/second2
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αavg=ω2 −ω1
Δt=
ΔωΔt
Rate of change of angular speed Counterclockwise => positive(+) Clockwise => negative(-)
Linear vs. Angular Quantities Linear
x
v
a
Angular
θ
•(m)
•(m/s)
•(m/s2)
• (rad)
• (rad/s)
• (rad/s2)
Linear vs. Angular Quantities Linear Angular
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f =ωi +αΔt
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Δθ = iΔt +1
2α (Δt)2
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f2 =ωi
2 + 2αΔθ
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Δθ =1
2(ωi +ω f )Δt
Warm-upA ceiling fan’s angular speed increases
from 5.2 rad/s to 20.9 rad/s. During this constant angular acceleration, the fan moves through an angular displacement of 216 rad. How long does it take the fan to reach its final angular speed?
Tangential Velocity Instantaneous linear speed of an object
tangent to a circular pathObjects with the same angular speed,
may have different tangential speedsm/s
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vt =rω
Tangential Acceleration Instantaneous linear acceleration of an
object tangent to a circular pathObjects with the same angular
acceleration, may have different tangential accelerations
m/s2
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at =rα
Total AccelerationTangential and centripetal acceleration
are perpendicular to one another
Use Pythagorean’s theorem to find the total acceleration.Angle ϕ is measured relative to the radius.
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