Classical Mechanics

• Kinematics – how objects move– Translational motion

– Rotational motion

– Vibrational motion

• Dynamics – Forces and why objects move as they do– Statics – special case -

forces cause no motion

Reference Frames• Position, distance or speed must be

specified wrt some reference frame.• Coordinate axis• Position = coordinate• Displacement = change in position

– final minus initial

• Displacement is a vector! Direction is from the initial to final position.

2 1x x x

Average Velocity

2 1

2 1

x xxv

t t t

More Examples

2 1

2 1

x xxv

t t t

t 0

x dxv lim

t dt

Velocity

• Average velocity

• Instantaneous velocity

2 1

2 1

x xxv

t t t

t 0

x dxv lim

t dt

Velocity vs. Speed?L

T

Instantaneous Velocity

t 0

x dxv lim

t dt

Acceleration

• Average acceleration

• Instantaneous acceleration

2 1

2 1

v v va

t t t

t 0

v dva lim

t dt

2

2

dv d dx d xa

dt dt dt dt

2

L

T

Example Problem 1

• A jogger runs in a straight line with – an average velocity of 5.00 m/s for 4.00 min.– an average velocity of 4.00 m/s for 3.00 min.

• What is her total displacement?

• What is her average velocity during this time?

Example Problem 2

• A particle moves along the x-axis acording to the equation (x is in meters, and t is in seconds):

• What must be the units on the constants?• What is the instantaneous velocity at t = 3.0 s?• What is the instantaneous acceleration at t = 3.0 s?• What is the displacement between t = 2.0 s and t = 3.0 s?• What is the average velocity between t = 2.0 s and t = 3.0 s?

2x 2t 3t

Motion Diagrams

See Wiley Plus Concept Simulation1D constant accelerationDifference between constant acceleration and constant velocity

What if acceleration is known?

t

0

0

v v adt t

0

0

x x vdt

Memory Aid

x, x

v, v

a

dx

dt

dv

dt

2

2

d xa

dt

adt

vdt

Constant Acceleration

0v v at

20 0

1x x v t at

2

2 20 0v v 2a x x

0v vv

2

Example Problem 3

• A car will go 0 to 87 mph in 8 sec. Assume the acceleration is constant.

• Find the acceleration

• Find the position after 8 sec.

• Find the velocity after 10 sec.

Falling Objects

• Galileo: at a given location on the earth and in the absence of air resistance, all objects fall with the same constant acceleration.

2

mg 9.8

s

• A person throws a ball upward into the air with an initial velocity of 15.0 m/s.

• Find:– How high it goes

– How long the ball is in the air before it comes back to his hand

– How much time it takes to reach maximum height

– The velocity of the ball when it returns to the throwers hand

– At what time the ball passes a point 8.00 m above the person’s hand.

Example Problem 4

The Graphs

Deceleration

• My golf ball goes flying in to the sandtrap at 30.0 m/s. It looks like a fried egg buried 3.00 cm into the sand. What was the acceleration of the golf ball caused by the sand as it landed?

Homework

• Wiley Plus Chap 2