Physics 170 - MechanicsLecture 9

Relative Motion

Vector Motion withConstant Acceleration

Position as a function of time:

Velocity as a function of time:

QuestionWhich of the blue position vs.time graphs goes with this greenvelocity vs. time graph? Theparticle’s position at ti = 0 s isxi = −10 m.

Relative Motion The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds:

vgnd = 16.2 m/s vgnd = 13.8 m/s

Relative MotionThis also works in two dimensions:

Observer on ground: sees the sum of two motions one horizontal and one vertical

Example: Galilean Relativity

Observer in the moving frame system: sees only a vertical motion

Observer on ground: sees the sum of two motions one horizontal and one vertical

N.B. Without air resistance!

Relative Motion

Definition: An Inertial Reference Frame is any coordinate system (or frame of reference) that is either at rest or moving in some direction with a constant velocity.Example: a train or airplane moving forward with a constant speed.

Relative Motion

Amy, Bill, and Carlos all measure the velocity of the runner and the acceleration of the jet plane. The green velocity vectors are shown in Amy’s reference frame. What is the runner’s velocity? It depends on the frame of the observer.Amy: vR = 5 m/sBill: vR = 0 m/sCarlos: vR =−10 m/s

What about aplane?

Relative Position The position depends on the frame. A set of position observations in one frame can be transformed to get equivalent observations in another frame.

Relative Velocity

A

z

x

y

B y’

z’

x’

vAB

vpA

The velocity also depends on the frame. A set of velocity observations in one frame can be transformed to get equivalent observations in another frame.

Example: Crossing a River You are riding in a boat with a speed relative to the water of vbw = 6.1 m/s. The boat points at an angle of θ = 25° upstream on a river flowing at vwg = 1.4 m/s.

(a) What is your speed vbg and angle θbg

relative to the ground?

An “inertial frame” is defined to be any reference frame that is at rest or moving with a constant velocity.Consider how the acceleration transforms from frame S to frame S’, an inertial frame that is moving with constant velocity V relative to S. Velocities add, so

Galilean Relativity

Galilean Relativity: While position and velocity are frame-dependent, acceleration is observed to be the same in all inertial reference frames.