Forces and Motion

Motion

A change in position of an object over time, compared to a reference point.

Frame of reference

Your frame of reference (what you compare movement to).

Unit cancellation (dimensional analysis)

A method to convert between units by multiplying by conversion factors until units cancel.

Rule for unit cancellation

Write everything in one line, cancel units diagonally, and multiply conversion factors.

Conversion reminder

1 kilometer = 1000 meters (kilo means 1000).

Scalar quantity

Has only magnitude (size), no direction.

Examples of scalar quantities

Speed, distance, time, temperature.

Vector quantity

Has both magnitude and direction.

Examples of vector quantities

Velocity, displacement, acceleration, force.

Positive and negative signs in vectors

They show direction (e.g. + = forward/right, − = backward/left).

Distance

Total path traveled (scalar).

Displacement

Change in position (final − initial) (vector).

Possible units for distance/displacement

Meters (m), kilometers (km), centimeters (cm).

Difference between distance and displacement

Distance = total path; Displacement = straight-line change in position (can be 0 if you return to start).

Position vs Time (P-T) graph

How an object's position changes over time.

Axes on a Position vs Time graph

x-axis = time (s), y-axis = position (m).

Straight angled line on a P-T graph

Constant velocity (object moving steadily).

Curved line on a P-T graph

Changing velocity (acceleration).

Flat/horizontal line on a P-T graph

The object is not moving (at rest).

Formula for average speed

Speed = total distance ÷ total time.

Formula for average velocity

Velocity = displacement ÷ time.

Units for speed or velocity

m/s, km/h, cm/s, etc.

Difference between speed and velocity

Speed = scalar (no direction); Velocity = vector (has direction).

Constant velocity

Moving at the same speed in the same direction.

Velocity vs Time (V-T) graph

How velocity changes with time.

Slope on a V-T graph

Acceleration.

Formula for acceleration

a = (vf − vi) ÷ (tf − ti).

Units for acceleration

m/s² or km/h².

Positive acceleration

Speeding up.

Negative acceleration

Slowing down (deceleration).

Finding acceleration on a P-T graph

Look for a curved line instead of a straight one.

Finding acceleration on a V-T graph

Find the slope of the line.

Steps for solving motion word problems

1. Identify knowns/unknowns; 2. Pick the right formula; 3. Plug in values with units; 4. Cancel units; 5. Check direction/signs.

First Law of Motion

An object at rest stays at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by a net external force.

Second Law of Motion

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, often expressed with the formula F = ma.

Third Law of Motion

For every action, there is an equal and opposite reaction, meaning that forces always occur in pairs.

Inertia

The tendency of an object to resist changes in its state of motion, directly related to its mass.

Net Force

The vector sum of all forces acting on an object, determining its acceleration according to the second law.

Mass

A measure of the amount of matter in an object, which affects its inertia and the force required to accelerate it.

Acceleration

The rate of change of velocity of an object, which occurs when a net force acts on it.

Action-Reaction Pairs

Forces that two objects exert on each other, equal in magnitude and opposite in direction, as described by the third law.

Equilibrium

A state in which the net force acting on an object is zero, resulting in no acceleration.

Friction

A force that opposes the motion of an object, often affecting the net force and resulting acceleration.

Slope

Represents the average speed of an object over a given time interval on a position-time graph.

Position-Time Graph

A graphical representation showing an object's position as a function of time.

Average Speed

Calculated as the total distance traveled divided by the total time taken.

Horizontal Line

Represents a state of rest, where the position does not change over time.

Units of Slope

Typically expressed in units of distance per time, such as meters per second.

What is the formula for average acceleration?

Average acceleration = (Final velocity - Initial velocity) / Time elapsed.

What does the average acceleration formula calculate?

It calculates the change in velocity over a specified time period.

What is the formula for weight?

Weight is calculated using the formula: Weight = mass × gravitational acceleration (W = mg).

What is the sum of forces?

The sum of forces is the total of all forces acting on an object, often represented as ΣF.

What is net force?

Net force is the vector sum of all individual forces acting on an object, determining its acceleration.

How do you find the sum of forces and the net force?

To find the sum of forces, add all the forces acting on an object, considering their directions; the net force is the resultant of this sum.

Vector Quantity

A quantity that has both magnitude and direction, such as displacement or velocity.

Scalar Quantity

A quantity that only has magnitude and no direction, such as distance or mass.

Initial Position

The starting point of an object before it undergoes any movement.

Final Position

The endpoint of an object after it has moved from its initial position.

Magnitude

The size or length of a vector, representing how far an object has moved in a specific direction.

Direction

The orientation of a vector, indicating the path along which an object moves from its initial to final position.

Displacement Formula

A mathematical expression used to calculate displacement, often represented as final position minus initial position.

Time

The duration over which motion occurs, usually measured in seconds, minutes, or hours.

Formula for Average Speed

The mathematical expression used to calculate average speed, represented as Average Speed = Distance / Time.

Units of Speed

Common measurements for speed, including kilometers per hour (km/h), miles per hour (mph), and meters per second (m/s).

What is fluid friction?

Friction that occurs when an object moves through a gas or liquid.

What is static friction?

The friction that exists between a stationary object and the surface it's on, preventing motion.

What is kinetic friction?

The friction that occurs between two surfaces in relative motion.

What is rolling friction?

The friction that occurs when an object rolls over a surface.

What is sliding friction?

The friction that occurs when two surfaces slide against each other.