Section 7­2 notes.notebook
November 30, 2011
Tangential Speed ­ the instantaneous linear speed of an object directed along the tangent to the object's circular path.
Angular Displacement
Δθ = Δs
r
To achieve Tangential Speed divide both sides by the Δt
Δθ = Δs
Δt rΔt
The left side of the equation is equal to the angular speed (ω). The right side Δs divided by Δt will result in the tangential speed.
Tangential Speed
vt = rω
tangential speed = distance from axis x angular speed
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Section 7­2 notes.notebook
November 30, 2011
The radius of a CD in a computer is 0.0600m. If a microbe riding on the disc's rim has a tangential speed of 1.88 m/s, what is the disc's angular speed?
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Section 7­2 notes.notebook
November 30, 2011
Tangential Acceleration ­ the instantaneous linear acceleration of an object directed along the tangent to the object's circular path.
Tangential Acceleration at = rα
tangential acceleration = distance from the axis x angular acceleration
A spinning ride at a carnival has an angular acceleration of 0.50 rad/s2. How far from the center is a rider who has a tangential acceleration of 3.3 m/s?
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Section 7­2 notes.notebook
November 30, 2011
Centripetal Acceleration ­ acceleration directed toward the center of a circular path
Centripetal Acceleration
ac = vt2
r
ac = rω2
centripetal acceleration = (tangential speed)2
distance from axis
centripetal acceleration = distance from axis x (angular speed)2
A test car moves at a constant speed around a circular track. If the car is 48.2 m from the track's center and has a centripetal acceleration of 8.05 m/s2, what is its tangential speed?
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Section 7­2 notes.notebook
November 30, 2011
Tangential Acceleration and Centripetal Acceleration are not the same.
When both components exist the total acceleration can be found by using Pythagorean Theorem.
Centripetal Acceleration is acceleration to the center of the circular path.
Tangential Acceleration is tangent to the circular path.
The two accelerations would be perpendicular to each other and the magnitude then would be calculated by atotal2 = at2 + ac2
The direction can be calculated by using the inverse tangent function.
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θ = tan ac
at
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Section 7­2 notes.notebook
Assignment November 30, 2011
7E ­ all
7F ­ all
7G ­ all
Sect 7­2 Review ­ all
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