系统 SYSTEM interactions 相互作用 SURROUNDINGS 外界

How do we detect interactions? 检测 Blackboard

Interactions cause change. We focus on these two. Change in direction Change in speed Change of shape Change of phase Change of temperature Change of identity Interactions cause change.

Change in direction

Change in speed

Change in velocity means: Change in direction, or speed, or both. 速度

In other words, a constant velocity. Uniform motion is motion with a constant speed and a constant direction. In other words, a constant velocity.

Uniform motion implies no net interaction.

This is not obvious!

Aristotle 亚里士多德 (384 BC – 322 BC) He believed that the natural state of an object is to be motionless; any motion must be caused by a force. His ideas were accepted for 2000 years.

Galileo 伽利略 (1564– 1642) Showed that, in the absence of friction, or other forces, an object will keep moving forever. 摩擦力

Isaac Newton 牛顿 (1643 – 1727) “Isaac Newton was born on Christmas day, 1642, within a year of Galileo’s death. Newton was a short man, nearsighted, already silver-gray in his thirties, inattentive to personal appearance, incredibly forgetful, and probably forever virginal. This nervous, hypochondriacal, sensitive, pious, vulnerable man was one of the greatest geniuses to ever live. Among Newton’s many achievements was a theory of motion that withstood every test for over 200 years.” - E. Hecht, Physics: Calculus, chap 4

Newton’s First Law of Motion An object moves in a straight line and at constant speed, except to the extent that it interacts with other objects.

Newton’s First Law of Motion 任何物体都要保持其静止或匀速直线运动状态，直到外力迫使它改变运动状态为止。

Which of these particles did not interact with something? Your turn… Which of these particles did not interact with something? A B C D A and B

Note: Speed is always positive. Speed is a scalar Note: Speed is always positive. avg is short for average 平均

Velocity is a vector 速度 Units: m/s

Velocity is a vector Remember: Δ is the Greek letter Delta, and means ‘change in something’.

Units on both sides must match

Your turn… A bee flies in a straight line at constant speed. At 15.0 s after 9 AM, the bee’s position is <2, 4, 0> m. At a time 15.5 s after 9 AM, the bee’s position is <3, 3.5, 0> m. What is the average velocity of the bee? <6, 7, 0> m/s <0.193, 0.225, 0> m/s <0.5, -0.25, 0> m/s 2.236 m/s <2.0, -1.0, 0> m/s

Position update formula We can use this to predict the motion of an object, if we know (or can guess) vavg.

Your turn… At 12.18 s after 1:30 PM, a ball’s position is <20, 8, -12> m, and the ball’s velocity is <9, -4, 6> m/s. What is the position of the ball at 12.21 s after 1:30 PM? 24.75 m <20.27, 7.88, -11.82> m <0.27, -0.12, 0.18> m <129.62, -40.72, 61.08> m <129.89, -40.84, 61.26> m

Your turn… A ball travels through the air. Part of its trajectory is shown in red. Which arrow best represents the direction of the average velocity of the ball as it travels from location A to location B? (1, 2, 3 or 4)? 1 2 轨迹 3 B 4 A

Instantaneous velocity 瞬时 Instantaneous velocity Our first use of calculus. 微积分

Instantaneous velocity “the derivative of r with respect to t” 导数

Instantaneous velocity “the rate of change of r”

The derivative of a vector is actually three derivatives

Acceleration: rate of change of velocity 加速度 Units: m/s2

Acceleration: rate of change of velocity Average acceleration: Instantaneous acceleration:

Bumper car ride

Example The position of a bumper car is described as a function of time by: Find: (a) The displacement and average velocity between t = 1.0 s and t = 3.0 s.

Example The position of a bumper car is described as a function of time by: Find: (b) The instantaneous velocity of the car at t = 3.0 s.

Example The position of a bumper car is described as a function of time by: Find: (c) The instantaneous acceleration of the car at t = 3.0 s.

Momentum 动量

50 km/hr

Velocity by itself is not a good “measure of motion”. 50 km/hr

The “measure of motion” (momentum) must involve the mass… What about mass x velocity ? This is almost right, but not exactly! 质量

Thanks to Einstein, we now know the correct definition of momentum: Greek letter gamma depends on how close the velocity is to the speed of light c.

The value of γ is very close to 1, unless the velocity is extremely close to the speed of light.

Large Hadron Collider, in Switzerland Protons are accelerated to 0.999999991 c. γ = 7500!

As long as v << c:

QUIZ