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