SHORT QUIZ #2Suppose you are measuring your waistline with

a tape measure. The ends of the tape measure are as shown. Report the measurement with the correct significant figures. Convert the measurement in millimetres (1in = 2.54cm) and express it in scientific notation with 4 significant figures.

One-dimensional motion

Lecture #3June 20 2013

Physical assumptionsEvery theory has a set of assumptions which specify the scope of its validity.

One must be careful to know all the assumptions made to arrive at a particular conclusion

Relativity

Speed is close to speed of light.Length scales are very large.

Quantum mechanics

Mass and length scales are small

Zinc atom on a layer of copper oxide

Classical physics• speed of the object << the speed of

light• mass and length scales are

comparable to “everyday objects”. • Ex: Air resistance and Coriolis force

are neglected in projectile motion

Mathematical modelsMathematical models are used to idealize the physical system and simplify the calculations.

The accuracy of the solution is dependent on the faithfulness of the mathematical model to physical reality.

Free fall and projectile motion

Projectile as point object: neglect rotational motion and microscopic fluctuations

Reference framesIn solving motion problems, it is important to specify the reference frame. For most of our purposes, the reference frame is one or two dimensional and at rest.

MotionThe only thing that constant in this world is change. All particles comprising the universe are in constant motion.

Two states of (translational) motion

• Motion with constant velocity• Accelerated motion

Kinematics: Study of how objects move

• Position• Distance and displacement• (Instantaneous and Average) Speed

and velocity• (Instantaneous and Average)

Acceleration

PositionPosition

specifies where the

object is in space.

Distance versus displacement

Distance is the length of the trajectory of an object.

Displacement is the change in position of the object with respect to the origin.

Speed versus velocity: AverageAverage speed is the change in distance divided by change in time.

Average velocity is the change in displacement divided by change in time.

Speed versus velocity: Instantaneous

Instantaneous speed

Instantaneous velocity

Average and instantaneous acceleration

Average acceleration is the change in velocity divided by change in time.

Instantaneous acceleration:

Speeding up or slowing down?

VELOCITY

ACCELERATION

Speed up Slow down

Slow down Speed up

Equations of motion with constant acceleration

• Position:

• Velocity:

• Acceleration:

Free fall

Free fall motion assumptions:

1. The height is much smaller than the earth’s radius so that the acceleration is constant.

2. The apple is a point object; the motion is purely translational.

3. Only gravity influences the motion. Air resistance and other effects are neglected.

Free fall motionGiven any two information, say, an initial velocity and position, the whole kinematics of free fall motion can be worked out. Why two?

Interpreting motion plots

Projectile Motion isconstantly accelerated vertical motion

+ motion with constant horizontal

velocity

Horizontal and vertical motion are

independent.

THREE POINTS:1. In the analysis of the motion of an object, one

must know the underlying physical assumptions, use idealized models, and specify the reference frame.

2. The kinematics of an object can be described by the following scalar or vector quantities: position, distance, displacement, as well as, average and instantaneous speed, velocity and acceleration.

3. Free fall is the one-dimensional motion of objects under the influence of the Earth’s gravity only. If in two dimensions, we have projectile motion.