# Mechanics

### 1. Measurements

Students will know the fundamental units of measurement and be able to distinguish between basic and derived units.

1.1 Define and analyze the concepts of space, time and matter.

1.2 Describe the basic units in the various systems of units (M.K.S., C.G.S., English & Technical). Use conversion factors to convert quantities from one system to another.

### 2. Vectors

The importance of vectors in physics and basic operations with them.

2.1 Define vector and scalar quantities and distinguish between them.

2.2 Determine rectangular components of a vector both graphically and analytically.

2.3 Find the magnitude and direction of a vector.

2.4 Calculate the resultant vector both graphically and analytically.

### 3. One-dimensional kinematics

Students will be able to describe the kinematics conditions of a body moving in a straight line with constant velocity or constant acceleration.

3.1 Position, path, displacement and distance covered.

3.2 Average velocity defined as the ratio of displacement and time; and average speed defined as the ratio of distance to time. (Note that ITESM official syllabus wrongly states that these are definitions of constant velocity and speed)

3.3 Apply the concepts of constant speed and constant velocity to solve given problems.

3.4 Instantaneous velocity and average velocity.

3.5 Acceleration defined as the change in velocity of a body with respect to time.(Note that ITESM official syllabus wrongly states that this is the definition of constant acceleration)

3.6 Algebraic equations that describe uniformly accelerated straight line motion.

3.7 Gravity.

3.8 The kinematics characteristics of the path followed by a body subject to gravity (vertical motion and free fall).

### 4. Two-dimensional Kinematics

4.1 Motion of projectiles.

The path followed by a body moving at a constant velocity and subject to a constant acceleration.

4.1.1 The gravitational effect on the path of a body which initially moves horizontally.

4.1.2 The equations that relate to a projectile fired horizontally.

4.1.3 The effect of gravity on a projectile fired horizontally.

4.1.4 Parabolic motion, problems involving parabolic motion

4.2 Circular motion

Circular motion as a particular case of two-dimensional motion and its relation with the translational motion.

4.2.1 The concept of angular displacement, its units (revolution, radian, cycle, degrees).

4.2.2 The relationship between angular and linear displacements.

4.2.3 The concepts of angular velocity and angular acceleration.

4.2.4 The relationship between constant angular velocity and constant tangential velocity and the corresponding equation. (This was quoted from the ITESM syllabus, but Mr. Ward asks whether 'constant tangential velocity' is actually possible..)

4.2.6 Equations for uniformly accelerated circular motion.

4.2.5 The relationship between tangential and angular acceleration.

4.2.7 Problems involving uniformly accelerated circular motion.

### 5. Particle dynamics

Newton's laws of mechanics and everyday applications.

5.1 Inertial mass.

5.2 Newton's first law (The law of inertia)

5.3 Newton's second law (The law of force)

5.4 Units of force.

5.5 The difference between mass and weight.

5.6 Newton's third law (Action-Reaction law).

5.7 Normal force (Orthogonal force) and centripetal force.

5.8 Friction.

5.9 Solve problems related to Newton's laws including incline planes.

5.10 Impulse and momentum.

### 6. Work and Energy

Explain work and its relationship with kinetic and potential energies and the concept of power.

6.1 Mechanical work and the equation that represents mechanical work.

6.2 The equation that represents mechanical work as the product of two vectors (dot product).

6.3 Problems involving mechanical work.

6.4 Kinetic and potential energies: two forms of mechanical energy.

6.5 The equations that represent potential and kinetic energy and their relationship with mechanical work.

6.6 Problems involving kinetic and potential energy.

6.7 Conservation of mechanical energy.

6.8 The equation for conservation of mechanical energy.

6.9 Solve problems related to the principle of conservation of mechanical energy.

6.10 Power and problems involving the concept of power.

### 7. Statics

Apply the concepts of force and torque on a body at equilibrium.

7.1 Define equilibrium.

7.2 Define translational equilibrium (ΣF = 0

7.3 Problems involving translational equilibrium:

7.4 Define rotational equilibrium (Στ = 0 ).

7.6 The concepts of lever arm and torque.

7.6 Solve problems related to both translation and rotational equilibrium.

### 8. Hydrostatics

The basic principles of hydrostatics.

8.1 Hydrostatics as part of mechanics.

8.2 Density.

8.3 Pressure given as the applied force per unit of area.

8.4 Archimedes and Pascal principles and hydrostatics problems.