Biomechanics: Vectors & Kinematics

Defining Vectors with Components

• Define a vector, r, from the (-6, 9) origin to (-6, 9). • Algebraic Definition: r 6 x 9 y • r = [-6x, 9y] • Convert this to • Magnitude and Direction

What are the 2 types of vectors?

- Magnitude and Direction (example) • Vs - Components [X ,Y] (example)

Example #1 of Vector vs. Scalar

A baseball player: His mass (a scalar) is the amount he weighs His weight (a vector) is the force exerted by his mass on the ground (directed downward).

What is a vector quantity?

A quantity with magnitude and direction! Vectors are designated by arrows: • The orientation (angle) of the arrow gives the direction. • The length of the arrow gives the magnitude.

What is a "scalar" quantity?

A quantity with magnitude only! Examples: - A ball player has a mass of 62kg. - The temperature outside is 87 deg. - A sprinter runs at speed of 1.5 m/s.

Example #2 of Vector vs. Scalar

A sprinter: Her speed (a scalar) is how fast she's running Her velocity (a vector) is her speed and direction (tangent to the track).

When dry friction acts between two surfaces that are moving relative to each other, it is referred to as

Dynamic Friction

Static friction is also referred to as

Limiting Friction

Vector Magnitude & Direction

Magnitude of r : • The vector, r, is the hypotenuse of a right triangle • Use Pythagorean Theorem. • Consider the angle defined by the vector relative to the +x axis.

Other terms for dynamic friction are

Sliding and Kinetic friction

When dry friction acts between two surfaces that are not moving relative to each other, it is referred to as

Static Friction

What is a vector?

a mathematical representation of anything that is defined by its size or magnitude (a number) and its direction (its orientation). To fully describe a force, you must describe its size and direction.

When an object speeds up, slows down, starts, stops, or changes direc- tion, it is

accelerating.

cos =

adjacent side over hypotenuse

Internal Forces

are forces that act within the object or system whose motion is being investigated. ex: The forces acting on a shot-putter and a shot at the instant before release.

Contact Forces

are forces that occur between objects in contact with each other. The objects in contact can be solid or fluid.

External Forces

are those forces that act on an object as a result of its interaction with the environment surrounding it. We can classify these as contact forces or noncontact forces.

General Motion

is a combination of linear and angular motions.

What is force?

is a push or a pull. Forces are exerted by objects on other objects. Forces come in pairs: The force exerted by one object on another is matched by an equal but oppositely directed force exerted by the second object on the first—action and reaction.

Angular Motion

is also referred to as rotary motion or rotation. It occurs when all points on a body or object move in circles (or parts of circles) about the same fixed central line or axis.

Linear Motion

is also referred to as translation. It occurs when all points on a body or object move the same distance, in the same direction, and at the same time. This can happen in two ways: rectilinear translation or curvilinear translation.

Linear Kinematics

is concerned with the description of linear motion. Questions about speed, distance, and direction are all inquiries about the linear kinematics of an object.

Average velocity

is defined as the change in velocity divided by the time it took for that velocity change to take place.

Dry Friction

is not affected by the size of the surface area in contact.

Friction

is parallel to the two surfaces in contact and opposes motion or sliding between the sur- faces.

Instantaneous acceleration

is the acceleration of an object at an instant in time

Weight

is the force of gravity acting on an object. W=mg g=9.8m/s^2

Displacement

is the straight-line distance in a specific direction from starting (initial) position to ending (final) position.

Rectilinear translation

occurs when all points on a body or object move in a straight line so that the direction of motion does not change, the orientation of the object does not change, and all points on the object move the same distance.

Curvilinear translation

occurs when all points on a body or object move so that the orientation of the object does not change and all points on the object move the same distance. The difference between rectilinear and this translation is that the paths followed by the points on an object in this translation are curved, so the direction of motion of the object is constantly changing, even though the orientation of the object does not change.

tan =

opposite side over adjacent side

sin =

opposite side over hypotenuse

If the object is at rest, the forces are in equilibrium and the object is described as being in a state of

static equilibrium

Motion

the action or process of a change in position.

The arcsine, arccosine, and arctangent functions are used to compute one of the angles in a right triangle if

the lengths of any two sides are known.