PHY 001 (Physics I)

Lecture 4

Instructor: Dr. Mohamed Fouad Salem

mohamed.salem@gmail.com

Lecture 4

TextbookUniversity Physics, 12th edition, Young and Freedman

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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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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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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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Angular Velocity

• The instantaneous angular velocity is ωz = dθ/dt.

• A counterclockwise rotation is positive; a clockwise rotation is negative.

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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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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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Angular Velocity calculations (Example Solution)

(a)

(b)

(c)

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Angular Velocity calculations (Example Solution)

(d)

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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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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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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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Angular Acceleration calculations (Example Solution)

(a)

(b)

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Angular Acceleration Vector

• For a fixed rotation axis, the angular acceleration and angular velocity vectors both lie along that axis.

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Rotation with Constant Angular Acceleration

• The formulas of rotational motion have the same form as the linear motion, as shown in the following table.

Next Time

• Section 9-2 Continued

• Section 9-3

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Assignment # 3

• Section 9-2

10, 13, 15 and 18

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