Motion in Two Dimensions - General Physics I - Lecture Slides, Slides of Physics

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Chapter 3

Motion in Two Dimensions

Units of Chapter 3

-^ Components of Motion •^ Vector Addition and Subtraction •^ Projectile Motion •^ Relative Velocity

3.1 Components of Motion

The velocity components are: The magnitude of the velocity vector is:

3.1 Components of Motion

The components of the displacement are thengiven by:^ Note that the

x-^ and

y- components are

calculated separately.

3.1 Components of MotionIf the acceleration is notparallel to the velocity,the object will move in acurve:

3.2 Vector Addition and Subtraction Geometric methods of vector addition Triangle method:

3.2 Vector Addition and Subtraction^ Vector Components and the Analytical

Component Method

If you know A and B,here is how to find C:

3.2 Vector Addition and Subtraction The componentsof C are given by: Equivalently,

3.2 Vector Addition and Subtraction Vectors can be resolved into components andthe components added separately; thenrecombine to find the resultant.

3.2 Vector Addition and Subtraction This is done most easily if all vectors start at theorigin.

3.3 Projectile Motion

A projectile launched in an arbitrary directionmay have initial velocity components in boththe horizontal and vertical directions, but itsacceleration is still downward.

3.3 Projectile Motion

The vertical motion is the same as if the objectwere thrown straight up or down with the sameinitial

y^ velocity, and the horizontal velocity is constant.

3.3 Projectile Motion

With air resistance, the range is shortened,and the maximum range occurs at an angleless than 45°.

ANIMATION:

Air Resistance^ Shoot the Monkey

3.4 Relative Velocity

Velocity may bemeasured in anyinertial referenceframe. At top, thevelocities aremeasured relative tothe ground; atbottom they aremeasured relative tothe white car. ANIMATION:

Relative Motion