Ch. 1 - Kinematics and Dynamics

6% of MCAT Physics content

1.2 Vectors and Scalars

What is the difference between a vector and a scalar?

Vector have magnitude and direction

• ex. displacement, velocity, acceleration, force

• bolded = vector quantity

Scalar have only magnitude

• distance, speed, energy, pressure, mass

• italic = scalar quantity

Vector Addition technique

1. tip-to-tail method (resultant)

2. breaking vector into perpendicular components (horizontal and vertical)

   • x-component = Vcosθ

   • y-component = Vsinθ

   • Vector magnitude = Pythagorean theorem

   • angle of resultant θ = tan^-1 (Y/X)

Vector Subtraction technique

Adding vectors but in opposite direction to the first vector:

A - B = A + (-B)

with either tip-to-tail or component method

What happens when you multiply a vector by a scalar?

It changes the magnitude and may reverse the direction.

B = nA

What happens when you multiply a vector by a vector?

Generate a scalar (magnitude) quantity by using dot product (A · B):

A · B = |A| |B| cos θ

Generate a vector (magnitude and direction) quantity by using cross product (A X B) and right-hand rule:

A × B = |A| |B| sin θ

1.3 Displacement and Velocity

What is the difference between displacement (x or d) and distance (d)?

displacement is a vector representing the straight-line distance between start and end positions, path independent

distance is a scalar that is path dependent

What is the difference between velocity (v) and speed (s)?

velocity is a vector representation of the change in displacement over time

• SI units = m/s

• direction is the same as the displacement vector

speed is a scalar representation of the rate of distance over time

What is the difference between instantaneous velocity and instantaneous speed?

Instantaneous velocity is a vector; average velocity as the change in time (Δt) approaches zero

Instantaneous speed is the magnitude of that vector

• not always as speed accounts for total distance traveled whereas velocity does not

1.4 Forces and Acceleration

What is a force (F)?

vector quantity that is the pushing or pulling on objects with the potential to cause acceleration

• SI unit = Newton (N) = (kg*m)/s²

What is gravity?

an attractive force felt by all forms of matter

• all objects exert gravitational forces on each other

Magnitude of gravitational force between two objects:

F_g = (Gm₁m₂)/r²

• G = gravitational constant (6.67 × 10^-11 Nm²/kg²)

• inversely related to square of distance: r is halved then F_g is quadruple

• directly related: m₁ is doubled then F_g will double

What is the difference between static friction and kinetic friction?

Friction is a force that opposes movement of objects

• coefficient of friction (μ) is unitless

• normal force = perpendicular to the plane of contact of object and surface it rests on

Static friction (f_s) exists between stationary object and surface

• magnitude of static friction: 0 ≤ f_s ≤ μ_sN

• range of possible static friction values

• do not assume that objects that are stationary are experiencing a maximal friction

• increase contact area = increase frictional force

Kinetic friction (f_k) exists between sliding object and the surface

• ex. sliding on ice

• magnitude of kinetic friction: f_k = μ_kN

• constant kinetic friction value

• independent of surface area of contact and velocity of sliding object

What determines the coefficient of friction?

The materials in contact.

coefficient of static friction is higher than that of kinetic friction

• maximum value of static friction > constant value of kinetic friction

• It always requires more force to get an object to start sliding than it takes to keep an object sliding.

What is the difference between mass (m) and weight (F_g)?

Mass is a scalar quantity of inertia - the amount of matter in the object

• SI unit = kg

Weight is the gravitational force acting on a mass.

• force = vector quantity

• SI unit = newtons (N)

Define center of mass

weight of an object applied at a single point

for a system of particles distributed in all three dimensions: center of mass defined by three coordinates (xyz)

center of mass of a uniform object is at the geometric center of the object.

Define acceleration (a)

A vector representing the rate of change in velocity over time.

• SI unit = m/s²

Average acceleration: Δv over Δt

Instantaneous acceleration: average acceleration as Δt approaches zero

• velocity vs. time graph: tangent at any time indicates instantaneous acceleration at that time

• positive slope = +a in same direction as v

• negative slope = -a in opposite direction of v (deceleration)

1.5 Newton’s Laws

What does Newton's First Law state (law of inertia)?

An object remains at rest or in constant velocity if no net force acts on it

What does Newton's Second Law state?

Acceleration is the result of the net force divided by the object’s mass.

• No acceleration will occur when the vector sum of the forces results cancels

• net force and acceleration vectors in same direction

What does Newton's Third Law state (law of action and reaction)?

Any two objects interacting exert equal and opposite forces on each other.

• Physical contact is not necessary; the mutual gravitational pull between the Earth and the Moon

1.6 Motion with Constant Acceleration

Describe linear motion.

Motion where velocity and acceleration are parallel or antiparallel, including free fall.

What forces act during projectile motion?

Gravity is the only force if air resistance is negligible.

How is motion on an inclined plane analyzed?

By breaking it into parallel and perpendicular components relative to the surface.

What defines uniform circular motion?

The centripetal force points radially inward, while instantaneous velocity is tangential.

What is translational equilibrium?

When the net force is zero

Object has constant velocity and may or may not be in rotational equilibrium.

What is rotational equilibrium?

When the net torque is zero

Object has constant angular velocity (usually zero on the MCAT)

What are free-body diagrams?

Visual representations of all forces acting on an object, useful for solving equilibrium and dynamics problems.