Linear Kinematics

Displacement Velocity and Acceleration

WOD are underlined

Linear KinematicsKinematics = “ the study of motion”

Forms of Motion

1. Linear

• translation

• all points on the body move the same distance in the same direction in the same amount of time

2. Angular

• rotation

3. General

• translation and rotation

Linear Kinematics

Kinematics = “ the study of motion”

Forms of Motion

1. Linear

Translation

2. Angular

rotation

New Terms• Distance –

• length of path travelled.

• Scalar (number only.)

• In meters

• Displacement-

• Change in position from start to stop.

• Vector (number and direction.)• Also in meters Walk around desk. How far did you go?

Distance

• What is the distance traveled in this picture?

Distance

• What is the displacement of the person in this picture?

Distance

• What is the displacement of the person in this picture?

• Displacement: DOES NOT CARE ABOUT PATH. START TO STOP!!!

• Where is 0 degrees for a Vector? • Is 0 Deg always +X??? No.

+X = 0 Deg or East

-X = 180 Deg

-Y = 270 Deg

+Y = 90 Deg

Negative Displacement

• What does positive vs negative:• Mean for Distance?• Mean for Displacement?

5m at 37 °

-5m at 37 °

Distance and Displacement

Starting from origin O, a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance?

Distance and Displacement

Starting from origin O, a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance? A: 130-m

Distance and Displacement

Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance? A: 130-m

Q: What is the displacement?

Distance and Displacement

Starting from origin, O a person walks 90-m east, then turns around and walks 40-m west.

Q: What is the total walked distance? A: 130-m

Q: What is the displacement? A: 50-m, due east. (or at 0 deg)

New Symbol• Δ – “Delta”

• Means “change in”• Final value – initial value

• Δa = change in a = af – ai

• Δd = change in d = df – di

• Δv = change in v = vf – vi

• Etc.

New Symbol

• So:

• x is horizontal position

• Δx is “change in x”

• Δx is “horizontal displacement”

• Δy is “vertical displacement”

• If someone is at x = 5,

• What distance have they traveled?

• (start at origin)

• If someone is at x = 5,

• What displacement have they traveled?

• (start at origin)

+X = 5

• If someone is at x = 5,

• What displacement have they traveled?

• (start at origin)

• 5m @ 0 degrees.

Displacement

The displacement x is a vector that points from the initial position xi to the

final position xf. x = xf - xi

SI Unit of Displacement: meter (m) and direction (angle in radians or deg).

• What is a radian???

+X = 0 or 2 π or East

-X = π

-Y = 3π/2

+Y = π/2

Question:

• The Earth is 1.5 * 1011 meters from the sun.

1.) If the orbit is a perfect circle, what is the distance the earth moves in six months?

2.) What is the displacement?

Question:

• The Earth is 1.5 * 1011 meters from the sun.

• If the orbit is a perfect circle, what is the distance the earth moves in six months?

• 1 half orbit = 2 r /2 = (3.14)* 1.5 * 1011 = 4.7 * 1011 m

• What is the displacement?

• Twice the radius = 2 *1.5* 1011 = 3.0 * 1011 m

Question:

• The Earth is 1.5 * 1011 meters from the sun.

• If the orbit is a perfect circle, what is the distance the earth moves in twelve months?

• What is the displacement?

Question:

• The Earth is 1.5 * 1011 meters from the sun.

• If the orbit is a perfect circle, what is the distance the earth moves in twelve months?

• 1 full orbit = 2 r = 2*(3.14)* 1.5 * 1011 = 9.4 * 1011 m

• What is the displacement?

• 0. It has made a full circle to its starting point