# Motion

##### by emily esser 10/03/2007

# Motion

by emily esser# 1. Acceleration

## 1.1. the rate of change of the velocity

## 1.2. indicates any change in the velocity vector

### 1.2.1. change in direction

### 1.2.2. increase in speed

### 1.2.3. decrease in speed

### 1.2.4. simultaneous change in speed and direction

## 1.3. To find it:

### 1.3.1. the change in velocity divided by the corresponding time interval

### 1.3.2. meters per second squared

## 1.4. Reading graphs

### 1.4.1. net force and velocity point in opposite directions=slowing down

### 1.4.2. Net force and velocity point in same direction= speeding up

### 1.4.3. Straight-line motion= acceleration is wither same direction as velocity or in the opposite direction to the velocity

# 2. Position

## 2.1. States where an object is located

## 2.2. x-, y-, and z-coordinates

## 2.3. Point of reference in relation to origin

### 2.3.1. Direction

### 2.3.2. Distance

# 3. Displacement

## 3.1. Definition:The change of the position vector

## 3.2. How to find it: The final position vector minus the initial position vector

## 3.3. Remember: does not necessarily equal the total distance traveled

# 4. Velocity

## 4.1. depends on displacement and time interval

## 4.2. Average velocity

### 4.2.1. does not reveal information about the motion during the time interval

### 4.2.2. product of the vector, the displacement, and a positive scalar, the inverse of the time interval

### 4.2.3. x-axis

4.2.3.1. represented on the graph as x(t)

## 4.3. Instantaneous velocity

### 4.3.1. a vector

### 4.3.2. magnitude is the speed

### 4.3.3. direction of motion

### 4.3.4. used to calculate the displacement of the object during a very short interval

## 4.4. Reading Graphs

### 4.4.1. sloping portions on graphs indicate=movement

### 4.4.2. a horizontal position=position has not changed

### 4.4.3. steeper the graph=faster speed

### 4.4.4. sign of the slope indicates direction of motion

4.4.4.1. positive slope

4.4.4.2. positive slope=motion in the +x-direction

4.4.4.3. negative slope=motion in the -x-direction

# 5. Newton's second law

## 5.1. rate of change of the velocity is proportional to the net force and inversely proportional to the mass of th object

## 5.2. net force is constant the acceleration is also constant

## 5.3. Applying to problems

### 5.3.1. Decide what objects will have Newton's second law applied to them

### 5.3.2. Identify all the external forces acting on that object

### 5.3.3. Draw a FBD to show all the forces acting on the object

### 5.3.4. Choose a coordinate system

### 5.3.5. find the net force by adding the forces as vectors

### 5.3.6. Relate the net force to acceleration

### 5.3.7. Relate the acceleration to the change in the velocity vector during a time interval of interest

# 6. Constant net force

## 6.1. equations

### 6.1.1. change of velocity is equal to the final velocity minus the initial velocity = acceleration times the change in time

### 6.1.2. refer to page 108 and 109

# 7. Visualization

## 7.1. Motion diagrams

### 7.1.1. position

### 7.1.2. velocity

### 7.1.3. Acceleration

# 8. Free Fall

## 8.1. No forces act on an object other than the gravitation force that makes the object fall

## 8.2. Air resistance

### 8.2.1. neglible

## 8.3. massive objects are harder to accelerate

## 8.4. More mass=more inertia

## 8.5. the acceleration of an object in free fall is the vector of "g" regardless of the object's mass

## 8.6. 9.80 meters per second squared

# 9. Motion of projectiles

## 9.1. an object moves in the xy-[plane with constant acceleration then both a of x and a of y are constant

## 9.2. Projectiles

### 9.2.1. objects in free fall

### 9.2.2. motion takes place in vertical plane

## 9.3. Angle of elevation

### 9.3.1. angle of initial velocity above the horizontal

## 9.4. Trajectory

### 9.4.1. path it takes in air

# 10. Apparent Weight

## 10.1. the feeling of "weightless"

## 10.2. elevator example

### 10.2.1. upwards the weight will be great than the true weight

### 10.2.2. downwards the weight will be less than the true weight

# 11. Air resistance

## 11.1. Drag force

### 11.1.1. increases as speed increases

### 11.1.2. the larger the surface area the more air is needed to be pushed out of the way

## 11.2. Terminal velocity

### 11.2.1. the acceleration is zero

## 11.3. Terminal speed

### 11.3.1. the magnitude of the terminal velocity is:

### 11.3.2. depends on:

11.3.2.1. size

11.3.2.2. shape

11.3.2.3. mass

# 12. Vectors

## 12.1. Positions and displacements

## 12.2. Problem solving

### 12.2.1. Vectors in different direction, Subtraction: is to add its opposite

12.2.1.1. has same magnitude but opposite direction

### 12.2.2. Multiplication

12.2.2.1. multiplyig a vector by the scalar -1 reverses the vector's direction while magnitude is unaffected