MCAT Physics · Lesson 1

Kinematics and Dynamics

4 min read6 sectionsUpdated January 3, 2026

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1.2Right Hand Rule
1.3Displacement and Velocity
1.4Forces and Acceleration
1.5Newton's Laws
1.6Motion with Constant Acceleration
1.7Mechanical Equilibrium

6 sections

1.2 Right Hand Rule

This section explains the right-hand rule for determining the direction of a cross product, the basics of vector operations, and distinctions between dot and cross products.

Right Hand Rule
- Thumb → direction of A
- Fingers → direction of B
- Palm → direction of C
- Example:
  - C = A × B, D = B × A
  - A: X = -3 N, Y = 0
  - B: X = 0, Y = 4 N
  - Magnitude: 12
  - Angle between vectors: 90°, sin 90° = 1
  - C → into page, D → out of page
Vector Operations
- Vector addition is commutative: A + B = B + A
- Vector subtraction is not commutative: same magnitude, different direction
Dot Product
- Produces a scalar from two vectors
- Formula: $A \cdot B = |A||B|\cos \theta$
Cross Product
- Use right-hand rule for direction
- Formula: $A \times B = |A||B|\sin \theta$
- Result is always perpendicular to the plane of the two vectors → in or out of page

1.3 Displacement and Velocity

Covers definitions of speed, velocity, and displacement, highlighting the difference between scalars and vectors, and average vs instantaneous values.

Instantaneous speed = instantaneous velocity (scalar)
Speed = magnitude of velocity vector
Average velocity = change in position / time
- If net displacement = 0 → average velocity = 0 (e.g., rotation of Earth)
Velocity ( $\vec{v}$ ) = rate of change of displacement

1.4 Forces and Acceleration

Introduces Newtonian mechanics, units of force, friction types, acceleration, and equilibrium concepts.

Force
- Unit: N = kg·m/s²
- $F = ma$
- Gravitational constant: $G = 6.67 \times 10^{-11}\ \mathrm{Nm^2/kg^2}$
Static Friction
- Between stationary object & surface
- $0 < F_\text{static} < \mu_s N$
- Coefficient $\mu_s$ depends on materials
- Friction opposes motion
- Max static friction example: 50 N < F_max < 100 N
Kinetic Friction
- Between sliding object & surface
- Formula: $F_\text{kinetic} = \mu_k N$
- Constant value, independent of surface area & velocity
- $\mu_s > \mu_k$ → moving objects slide easier
Inclined Planes
- Friction depends on normal force
- As incline ↑ → normal force ↓ → frictional force ↓
Acceleration
- Average: Δv/Δt
- Instantaneous: $\lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t}$
- Positive slope on v-t graph → acceleration in same direction
- No force → no acceleration, constant velocity
- Translational equilibrium: forces equal in magnitude

1.5 Newton's Laws

Covers the three fundamental laws of motion describing inertia, acceleration, and action-reaction pairs.

First Law (Inertia)
- $F = ma = 0$
- Object at rest or in motion remains so
Second Law
- $F_\text{net} = ma$
- Acceleration occurs when net force ≠ 0
- Direction of acceleration = direction of net force
Third Law
- $F_{AB} = -F_{BA}$
- Every action → equal & opposite reaction

1.6 Motion with Constant Acceleration

Explains linear, projectile, and circular motion, including free fall and kinematics equations for constant acceleration.

Linear Motion
- Equations of motion:
  - $v = v_0 + at$
  - $x = v_0 t + \frac{1}{2} a t^2$
  - $v^2 = v_0^2 + 2 a x$
  - $x = vt$
- Positive motion → downward negative
- Constant acceleration if air resistance negligible
Free Fall
- Drag neglected → constant acceleration = $g$
- Drag present → acceleration ↓ until terminal velocity
Projectile Motion
- Force only in vertical direction
- Time in flight: $Y = v_0 t + \frac{1}{2} a t^2$ , set Y = 0
- X-component: $X = v_0 t + \frac{1}{2} a t^2$
- Max horizontal distance at 45° angle
Circular Motion
- Displacement = 0 after one cycle
- Uniform circular motion:
  - Instantaneous velocity tangent to path
  - Centripetal force points radially inward: $F_c = \frac{mv^2}{r}$
- Centrifugal force: reactionary, antiparallel to centripetal

1.7 Mechanical Equilibrium

Discusses rotational equilibrium, torque, and conditions for static equilibrium.

Rotational Equilibrium
- Force applied to rotate around fulcrum → creates torque
- Lever arm = distance from force to pivot
- Torque formula: $\tau = r \times F = r F \sin \theta$
- Equilibrium → vector sum of torques = 0
- Clockwise → negative, counterclockwise → positive
Example:
- Force exerted by fulcrum = combined mass of blocks & seesaw × $F_g$

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