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
Average angular velocity
Instantaneous angular velocity
Average angular acceleration
Instantaneous angular acceleration
Relating the linear and angular variables
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
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
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 tan−1
= θ
8.5 Newton’s universal law of gravitation
Gravitation near Earth’s surface
Free-fall acceleration…
Taken from Halliday
Ex
Taken from Halliday
Sol:
8.6 Kepler’s laws
Special case: A circular orbit
Exercises: 8.5, 8.31
Chapter 9 Rotational Motion and Angular Momentum
9.2 Kinematics of Rotational Motion
9.3 Rotational Inertia
Calculating the rotational inertia
Many cases… ..
Ex
proof)
Angular Momentum
Conservation of Angular Momentum
Ex
Taken from Halliday
Exercises: 9.10, 9.20
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!!
Taken from Halliday
10.4 Variation of pressure with depth in a fluid
Fluid at rest
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.
Pascal’s Principle
Taken from Halliday
10.7 Archimede’s Principle
11.1 Bernoulli’s Equation
Proof
Taken from Halliday
Exercises: 10.19, 10.42
