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

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Presentation transcript:

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

This formula is the key to simulating motion with computer programs. 模拟 1.Calculate new r 2.Calculate new v avg (how?...) 3.Next time step

My research: simulating the motion of proteins 蛋白质 Proteins are the molecular machines that must work to keep living things alive. Many diseases are caused by ‘broken’ proteins.

Special case: constant acceleration A common example of constant acceleration: falling.

Which direction is the acceleration?

Parallel (or anti-parallel) to the velocity, changing the speed. 平行

Which direction is the acceleration? Perpendicular to the velocity, changing the direction of motion. 垂直

Curved motion

Acceleration can be split into two types: (1) Acceleration that changes speed, and not direction (2) Acceleration that changes direction, and not speed

Acceleration can be split into two types: Change in speed: tangential acceleration a t Change in direction: radial acceleration a r

Let’s calculate a r.

θ R R After a time Δt, particle moves to position 2. RR θ θ 1 1 These are similar triangles.

θ R R After a time Δt, particle moves to position 2. RR θ θ 11 These are similar triangles.

RR θ θ 11 These are similar triangles, so:

The radial acceleration is also called centripetal acceleration. Its magnitude is 向心加速度 and its direction is towards the center of the circle.

Example: The Moon’s orbit around the Earth

Assume a circular orbit. (It’s really an ellipse.) 假设 R = 3.84 x 10 8 m Period of one orbit: T = 27.3 days