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# Chapter 8 Uniform circular motion and gravitation

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## Chapter 8 Uniform circular motion and gravitation

Many motions, such as the arc of a bird’s flight or the earth’s path around the sun are curved.

Uniform circular motion: motion in a circular path at constant speed.

8.1 Rotation Angle and Angular Velocity

Taken from Halliday

Taken from Halliday

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Average angular velocity

Instantaneous angular velocity

Average angular acceleration

Instantaneous angular acceleration

Relating the linear and angular variables

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The tangential component of the linear acceleration of the point

8.2 Centripetal acceleration

Taking the ratio of BC to BA in each triangle, we obtain

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2

1 v

v v= =

r r v

v = ∆

r r v= v

t r r v t v

= ∆

r a v t v

t

= 2

∆ =

8.3 Centripetal force

c

t F

r mv t ma

m v = = =

2

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Example

(a) Calculate the centripetal force exert on a 900 kg car that negotiates a 500 m radius curve at 25.0 m/s. (b) Assuming an unbanked curve, find the minimum static coefficient of friction between the tires and the road.

Sol:

a) (900 kg)(1.25 m/s2) 1125 N 1130 N

2 = = = ≈

= c

c ma

r mv F

b)

Friction is to the left, causing the car to turn; thus friction is the centripetal force in this case

r mv mg N

f

Fc s s

= 2

=

=

= µ µ

13 . 0

2 =

= rg v µs

Banked curve

r N mv

2

sinθ =

mg Ncosθ =

r mg mv

2

cos sin =

θ θ

rg v2 tan1

= θ

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8.5 Newton’s universal law of gravitation

Gravitation near Earth’s surface

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Free-fall acceleration…

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Taken from Halliday

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Ex

Taken from Halliday

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Sol:

8.6 Kepler’s laws

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Special case: A circular orbit

Exercises: 8.5, 8.31

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## Chapter 9 Rotational Motion and Angular Momentum

9.2 Kinematics of Rotational Motion

9.3 Rotational Inertia

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Calculating the rotational inertia

Many cases… ..

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Ex

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proof)

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Angular Momentum

Conservation of Angular Momentum

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Ex

Taken from Halliday

Exercises: 9.10, 9.20

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Chapter 10 Fluid Statics

10.1 What is a fluid

Fluids flow. More precisely, a fluid is a state of matter that yields to sideways or shearing forces.

Solid and liquid

10.2 Density

10.3 Pressure

A scalar!!

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Taken from Halliday

10.4 Variation of pressure with depth in a fluid

Fluid at rest

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Mercury barometer

Mercury Manometers

By squeezing the bulb, the person making the measurement creates pressure, which is transmitted undiminished to both the main artery in the arm and the manometer. When this applied pressure exceeds blood pressure, blood flow below the cuff is cut off. The person making the measurement then slowly lowers the applied pressure and listens for blood flow to resume. Blood pressure sure pulsates because of the pumping action of the hear, reaching a maximum, called systolic pressure, and a minimum, called diastolic pressure, with each heartbeat.

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Pascal’s Principle

Taken from Halliday

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10.7 Archimede’s Principle

11.1 Bernoulli’s Equation

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Proof

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Taken from Halliday

Exercises: 10.19, 10.42

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