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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 QuantitySymbolSI Unit Massmkg Lengthlm Timets 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 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. The number of digits between the Most significant figure and least significant figure inclusive.

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

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Accuracy and Precision Accuracy –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 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 v t 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 v t acceleration: slope=g at t=0 uniform speed: slope = 0

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

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

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v-t graph of a bouncing ball Large acceleration on rebound v t falling rebound

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

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v-t graph of a bouncing ball Uniform acceleration: slope = -g v t falling rebound rising

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

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Linear Motion: Motion along a straight line Uniformly accelerated motion: a = constant velocity time v u t0

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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 time v u t0 velocity

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Uniformly accelerated motion time v u t0 velocity s = displacement = 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 gun bullet aluminium foil electromagne t iron ball

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Monkey and Hunter Experiment gun bullet aluminium foil electromagne t iron ball The bullet breaks the aluminium foil.

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Monkey and Hunter Experiment gun bullet electromagne t iron ball Bullet moves under gravity. Iron ball begins to drop.

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Monkey and Hunter Experiment gun bullet electromagne t Bullet is moving under gravity. Iron ball is dropping under gravity.

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Monkey and Hunter Experiment gun electromagne t

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Monkey and Hunter Experiment gun electromagne t 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 y x

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y x

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y x u u = initial velocity = initial angle of inclination

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

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Projectile trajectory y x u = x-component of u = y-component of u

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Projectile trajectory y x u

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Projectile trajectory: accelerations y x u

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

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Projectile trajectory: velocity in horizontal direction y x u v Horizontal line

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Projectile trajectory: velocity in vertical direction y x u v vertical line Horizontal line

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Projectile trajectory: displacement y x x = x-component of s y = y-component of s s s = displacement

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Projectile trajectory: horizontal displacement y x s s = displacement

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Projectile trajectory: vertical displacement y x s s = displacement

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Equation of trajectory: a parabolic path y x s s = displacement

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

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Projectile trajectory: direction of motion y x u v Horizontal line vertical line

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Projectile trajectory Example 19

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Projectile trajectory: maximum height H y x u H At H, = 0

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Projectile trajectory: range R y x u At R, y = 0 R

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Projectile trajectory: maximum range R max y x u R max is maximum when

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Projectile trajectory: maximum range R max y x u R max R is maximum when

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Projectile trajectory: maximum range R max y x u R max

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Projectile trajectory: time of flight t o y x u At time= t o, y = 0 R toto

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Projectile trajectory: two angles for one range y x 1 R 2 u u 1 = - 2

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