Chapter 3

Nonlinear Motion

1. MOTION IS RELATIVE

Example: Motion of a boat with respect to the ground and with respect to the river.

Velocity of river

Velocity of boat with respect to river

Velocity of boat with respect to ground

Add the velocity of the river

Velocity of river

Velocity of boat with respect to river

Velocity of boat with respect to ground

Add the velocity of the river

Velocity of river

Velocity of boat with respect to river

Velocity of boat with respect to ground

2. VELOCITY - A VECTOR QUANTITY

Scalars are quantities that are specified by magnitude only.

Examples: distance, time, mass, density Vectors are quantities that are specified by

magnitude and direction. Examples: displacement, velocity,

acceleration, force, momentum, angular momentum

4 miles east

3 miles north5 miles

370 north of east

The Displacement Vector

What is the displacementfor this trip?

3. PROJECTILE MOTION

Projectile motion is a combination of

vertical free-fall motion and horizontal

motion at a constant speed.

Parabola (approximately)

Demo - Ball projector and dropperDemo - Ball projector and dropper

Demo - Monkey in treeDemo - Monkey in tree

Demo - Cart and ball launcherDemo - Cart and ball launcher

Demo - Wall parabolaDemo - Wall parabola

The free-fall motion of a projectile near the surface of the earth is very nearly parabolic.

A parabola is one of the of a conic sections.

Circle Ellipse Parabola Hyperbola

For a particular range less than the maximum

and for a particular launch velocity,

two different launch angles will give that range.

The two angles add to give 900.

450 gives the maximum range.

Simulation

Free Fall Results

Horizontal motion is constant Vertical Motion is accelerated Rise time = Fall Time Final speed = Initial speed

Actual path and ideal path (free fall) are different.

4. FAST-MOVING PROJECTILES - SATELLITES

Lets throw stones horizontally with ever

increasing velocity.

The Earth’s curvature is 16 ft for every 5 miles

(4.9 m for 8 km).

16 ft

16 ftCurvature of Earth

5 miles

Throw an object faster, faster.faster,

We draw in each trajectory for 1 second

Ellipse

Ellipse

Ellipse - Circle

Ellipse

Ellipse

Parabola

Vcircle = 5 mi/s = 8 km/s Vescape = 7 mi/s = 11 km/s

Hyperbola

4. CIRCULAR MOTION

Linear speed and rotational speed

Linear speed is a distance divided by time.

Rotational speed is an angle measurement

divided by time.

A B

Which fly has thegreater linear speed?

B

Which fly has the greater rotational speed?

Same for both.

A

B

AB

AB

A

B

A

B

Two Flies on a Turntable

Chapter 3 Review Questions

A rock is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? (Neglect air resistance.)

(a) it decreases

(b) it increases

(c) it remains the same

(c) it remains the same

In the game of baseball which path would a home run most closely approximate? (Neglect air resistance.)(a) hyperbolic

(b) parabolic

(c) eccentric

(b) parabolic

A projectile is launched upward at an angle of 75o from the horizontal and strikes the ground a certain distance down range. What other angle of launch at the same launch speed would produce the same distance? (Neglect air resistance.)(a) 450

(b) 150

(c) 250

(b) 150

A horizontally traveling car drives off of a cliff next to the ocean. At the same time that the car leaves the cliff a bystander drops his camera. Which hits the ocean first? (Neglect air resistance.)

(a) car

(b) camera

(c) they both hit at the same time

(c) they both hit at the same time

Bug A is 3 inches from the center of a rotating 33.33 rpm record. Bug B is 5 inches from the center of the same record. Bug A has           linear speed and           rotational speed as bug B.(a) less, less

(b) less, same

(c) same, less

(d) same, same

(e) less, greater

(b) less, same