unit 8: circular motion. section a: angular units corresponding textbook sections: –10.1 pa...
TRANSCRIPT
![Page 1: Unit 8: Circular Motion. Section A: Angular Units Corresponding Textbook Sections: –10.1 PA Assessment Anchors: –S11.C.3.1](https://reader035.vdocuments.us/reader035/viewer/2022062423/5697bfc81a28abf838ca8a00/html5/thumbnails/1.jpg)
Unit 8: Circular Motion
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Section A: Angular Units
Corresponding Textbook Sections:– 10.1
PA Assessment Anchors:– S11.C.3.1
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Angular Position
Defined as the angle, , that a line from the axle to a spot on the wheel makes with a reference line
Unit: Radian (rad)
[dimensionless]
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Sign convention for angular position:
If > 0, counterclockwise rotation
If < 0, clockwise rotation
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Converting between degrees and radians
1 revolution = 360 = 2 rad
1 rad = 57.3
Convert the same way you would between any other units.
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Section B: Angular / Linear Relationships
Corresponding Textbook Sections:– 10.3
PA Assessment Anchors:– S11.C.3.1
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Arc Length
The arc length is the distance from a reference line to a spot of interest on a circle.
Equation:
s = r
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Angular Velocity
Symbol:
Units: s-1 or 1/s
€
av =Δθ
Δt
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Sign Convention for
If > 0 Counterclockwise rotation
If < 0 Clockwise rotation
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Practice Problem #1
An old phonograph rotates clockwise at 33⅓ rpm. What is the angular velocity in rad/s?
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Practice Problem #2
If a CD rotates at 22 rad/s, what is its angular speed in rpm?
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Period
The period is the time it takes to complete one revolution.
Units: seconds (s)
€
T = 2π
ω
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Practice Problem #3
Find the period of a record that is rotating at 45 rpm.
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Angular Acceleration
The change in angular speed of a rotating object per unit of time.
Units: rad/s2
€
α =ΔΔt
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Practice Problem #4
As the wind dies, a windmill that was rotating at 2.1 rad/s begins to slow down with a constant angular acceleration of 0.45 rad/s2. How long does it take for the windmill to come to a complete stop?
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Section C: Angular Kinematics
Corresponding Textbook Sections:– 10.2
PA Assessment Anchors:– S11.C.3.1
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Relationship between angular and linear quantities
Linear Quantity Angular Quantity
x
v ω
a α
Based on these relationships, we can rewrite thekinematics equations from 1-D and 2-D Kinematics
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Angular Kinematics Equations
€
v = vo + at ω =ωo +αt
x = xo + vot +1
2at 2 θ =θo +ωot +
1
2αt 2
v 2 = vo2 + 2aΔx ω2 =ωo
2 + 2αΔθ
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So, basically…
These are just variations of equations we already know how to use.
They work the same way as the linear equations.
We’ll use the same setup as before:• Data table, equation, picture, etc…
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Practice Problem #1
To throw a curveball, a pitcher gives the ball an initial angular speed of 36 rad/s. When the catcher gloves the ball 0.595 s later, its angular speed has decreased to 34.2 rad/s. What is the ball’s angular acceleration?
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Practice Problem #2
Based on the last problem, how many revolutions does the ball make before being caught?
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Practice Problem #2
Refer to Example 10-2 on page 280
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Section D: Torque
Corresponding Textbook Sections:– 11.1, 11.2
PA Assessment Anchors:– S11.C.3.1
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What is Torque?
Torque is the rotational equivalent of force
It depends on:– Force applied– Distance from the force to the axis of
rotation
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More on Torque…
Equation:
Units: Nm
€
τ =rFGreek Letter “tau”
Axis of Rotation(where it turns)
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Practice Problem #1
If the minimum required torque to open a door is 3.1 Nm, what force must be applied if:– r = 0.94 m– r = 0.35 m
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Section E: Moment of Inertia
Corresponding Textbook Sections:– 10.5
PA Assessment Anchors:– S11.C.3.1
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What is “Moment of Inertia”?
The “rotational mass” of an object– Rotational mass depends on actual mass,
radius, and distribution of mass
Useful for determining rotational KE:
€
KE =1
2Iω2
Moment of inertia
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Practice Problem #1
What is the moment of inertia of a hollow sphere with mass of 40 kg and radius of 3 m?
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Practice Problem #2
A grindstone with radius of 0.61 m is being used to sharpen an axe. If the linear speed of the stone relative to the ax is 1.5 m/s, and the stones rotational KE is 13 J, what is its moment of inertia?