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Lecture 4
TextbookUniversity Physics, 12th edition, Young and Freedman
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Lecture 4
Angular Coordinate
• A car’s speedometer needle rotates about a fixed axis, as shown at the right.
• The angle θ that the needle makes with the +x-axis is a coordinate for rotation.
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Lecture 4
Units of Angles
• An angle in radians is θ = s/r, as shown in the figure.
• One complete revolution is 360° = 2π radians.
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Lecture 4
Angular Velocity
• The angular displacement ∆θ of a body is ∆θ = θ2 – θ1.
• The average angular velocity of a body is ωav-z = ∆θ/∆t.
• The subscript z means that the rotation is about the z-axis.
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Lecture 4
Angular Velocity
• The instantaneous angular velocity is ωz = dθ/dt.
• A counterclockwise rotation is positive; a clockwise rotation is negative.
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Lecture 4
Angular Velocity calculations (Example)
• The angular position of a 0.36 m diameter flywheel is given by
(a) Find in radians and in degrees at
and
(b) Find the distance that a particle on the
flywheel rim moves over the interval from
to
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Lecture 4
Angular Velocity calculations (Example)
(c) Find the average angular velocity in rad/s
and rev/min over that interval.
(d) Find the instantaneous angular velocities
at and
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Lecture 4
Angular Velocity calculations (Example Solution)
(a)
(b)
(c)
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Lecture 4
Angular Velocity calculations (Example Solution)
(d)
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Lecture 4
Angular Velocity Vector • Angular velocity is defined as a vector whose
direction is given by the right-hand rule shown in the following figure
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Lecture 4
Angular Acceleration
• The average angular acceleration is αav-z = ∆ωz/∆t.
• The instantaneous angular acceleration is αz = dωz/dt = d2θ/dt2.
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Lecture 4
Angular Acceleration calculations (Previous Example Continued)
• In the previous example, find the
(a) Average angular acceleration between
and
(b) instantaneous acceleration at
and
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Lecture 4
Angular Acceleration calculations (Example Solution)
(a)
(b)
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Lecture 4
Angular Acceleration Vector
• For a fixed rotation axis, the angular acceleration and angular velocity vectors both lie along that axis.
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Lecture 4
Rotation with Constant Angular Acceleration
• The formulas of rotational motion have the same form as the linear motion, as shown in the following table.
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Next Time
• Section 9-2 Continued
• Section 9-3
Lecture 4
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Assignment # 3
• Section 9-2
10, 13, 15 and 18
Lecture 4