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Physics Beyond 2000 Chapter 1 Kinematics

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Physical Quantities Fundamental quantities Derived quantities

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**Fundamental Quantities**

Quantity Symbol SI Unit Mass m kg Length l Time t s Others -

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**Derived Quantities Can be expressed in terms of the basic quantities**

Examples Velocity Example 1 Any suggestions?

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Derived Quantities More examples

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**Standard Prefixes Use prefixes for large and small numbers Table 1-3**

Commonly used prefixes giga, mega, kilo centi, milli, micro, nana, pico

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Significant Figures The number of digits between the Most significant figure and least significant figure inclusive. The leftmost non-zero digit is the most significant figure. If there is no decimal point, the rightmost non-zero digit will be the least significant figure. If there is a decimal point, the rightmost digit is always the least significant figure.

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Scientific Notation Can indicate the number of significant numbers

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Significant Figures Examples 5 and 6. See if you understand them.

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**Significant Figures Multiplication or division.**

The least number of significant figures. Addition or subtraction. The smallest number of significant digits on the right side of the decimal point.

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Order of Magnitude Table 1-4.

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**Measurement Practice Length Meter rule Vernier caliper**

Micrometer screw gauge Practice

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Measurement Time interval Stop watch Ticker tape timer Timer scaler

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Measurement Mass Triple beam balance Electronic balance

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Measurement Computer data logging

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**Error Treatment Personal errors Random errors System errors**

Personal bias Random errors Poor sensitivity of the apparatus System errors Measuring instruments Techniques

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**Accuracy and Precision**

How close the measurement to the true value Precision Agreement among repeated measurements Largest probable error tells the precision of the measurement

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**Accuracy and Precision**

Examples 9 and 10

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**Accuracy and Precision**

Sum and difference The largest probable error is the sum of the probable errors of all the quantities. Example 11

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**Accuracy and Precision**

Product, quotient and power Derivatives needed

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Kinematics Distance d Displacement s

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Average Velocity Average velocity = displacement time taken

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**Instantaneous Velocity**

Rate of change of displacement in a very short time interval.

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Uniform Velocity Average velocity = Instantaneous velocity when the velocity is uniform.

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Speed Average speed Instantaneous speed

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Speed and Velocity Example 13

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**Relative Velocity The velocity of A relative to B**

The velocity of B relative to A

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Relative Velocity Example 14

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Acceleration Average acceleration Instantaneous acceleration

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**Average acceleration Example 15 Average acceleration =**

change in velocity time Example 15

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**Instantaneous acceleration**

Example 16

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**Velocity-time graph v-t graph**

Slope: = acceleration

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v-t graph Uniform velocity: slope = 0 v t

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v-t graph Uniform acceleration: slope = constant v t

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**Falling in viscous liquid**

Acceleration Uniform velocity

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**Falling in viscous liquid**

uniform speed: slope = 0 acceleration: slope=g at t=0 t

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**Bouncing ball with energy loss**

Let upward vector quantities be positive. Falling: with uniform acceleration a = -g.

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**v-t graph of a bouncing ball**

Uniform acceleration: slope = -g v t falling

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**Bouncing ball with energy loss**

Let upward vector quantities be positive. Rebound: with large acceleration a.

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**v-t graph of a bouncing ball**

Large acceleration on rebound v rebound t falling

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**Bouncing ball with energy loss**

Let upward vector quantities be positive. Rising: with uniform acceleration a = -g.

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**v-t graph of a bouncing ball**

Uniform acceleration: slope = -g v rebound rising t falling

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**v-t graph of a bouncing ball**

The speed is less after rebound falling and rising have the same acceleration: slope = -g v rebound rising t falling

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**Linear Motion: Motion along a straight line**

Uniformly accelerated motion: a = constant velocity v u time t

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**Uniformly accelerated motion**

u = initial velocity (velocity at time = 0). v = final velocity (velocity at time = t). a = acceleration v = u + at

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**Uniformly accelerated motion**

= average velocity velocity v u time t

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**Uniformly accelerated motion**

s = displacement = velocity v u time t s = area below the graph

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**Equations of uniformly accelerated motion**

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**Uniformly accelerated motion**

Example 17

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**Free falling: uniformly accelerated motion**

Let downward vector quantities be negative a = -g

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**Free falling: uniformly accelerated motion**

a = -g

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**Free falling: uniformly accelerated motion**

Example 18

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**Parabolic Motion Two dimensional motion under constant acceleration.**

There is acceleration perpendicular to the initial velocity Examples: Projectile motion under gravity. Electron moves into a uniform electric field.

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**Monkey and Hunter Experiment**

electromagnet gun aluminium foil bullet iron ball

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**Monkey and Hunter Experiment**

electromagnet gun aluminium foil bullet iron ball The bullet breaks the aluminium foil.

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**Monkey and Hunter Experiment**

electromagnet gun bullet iron ball Bullet moves under gravity. Iron ball begins to drop.

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**Monkey and Hunter Experiment**

electromagnet gun bullet Bullet is moving under gravity. Iron ball is dropping under gravity.

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**Monkey and Hunter Experiment**

electromagnet gun

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**Monkey and Hunter Experiment**

electromagnet gun The bullet hits the ball!

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**Monkey and Hunter Experiment**

The vertical motions of both the bullet and the iron are the same. The vertical motion of the bullet is independent of its horizontal motion.

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**Projectile trajectory**

x

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**Projectile trajectory**

x

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**Projectile trajectory**

u x u = initial velocity = initial angle of inclination

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**Projectile trajectory**

v Horizontal line u x v = velocity at time t = angle of velocity to the horizontal at time t

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**Projectile trajectory**

u x = x-component of u = y-component of u

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**Projectile trajectory**

u x

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**Projectile trajectory: accelerations**

u x

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**Projectile trajectory**

v Horizontal line u vertical line x = x-component of v = y-component of v

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**Projectile trajectory: velocity in horizontal direction**

Horizontal line u x

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**Projectile trajectory: velocity in vertical direction**

Horizontal line u vertical line x

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**Projectile trajectory: displacement**

s = displacement y s x x = x-component of s y = y-component of s

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**Projectile trajectory: horizontal displacement**

s = displacement y s x

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**Projectile trajectory: vertical displacement**

s = displacement y s x

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**Equation of trajectory: a parabolic path**

s = displacement y s x

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**Projectile trajectory: direction of motion**

v Horizontal line u vertical line Projectile trajectory x Angle represents the direction of motion at time t.

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**Projectile trajectory: direction of motion**

v Horizontal line u vertical line Projectile trajectory x

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**Projectile trajectory**

Example 19

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**Projectile trajectory: maximum height H**

x At H, = 0

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**Projectile trajectory: range R**

u R x At R, y = 0

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**Projectile trajectory: maximum range Rmax**

Rmax x is maximum when

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**Projectile trajectory: maximum range Rmax**

Rmax x R is maximum when

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**Projectile trajectory: maximum range Rmax**

Rmax x

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**Projectile trajectory: time of flight to**

u to R x At time= to , y = 0

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**Projectile trajectory: two angles for one range**

u u 2 1 R x 1= 2

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