Physics

Part I: Sections I-V

(Emphasis is on translational motion, force and motion, gravitation, work and energy, equilibrium and momentum, periodic motion and wave characteristics)


At the beginning of each of the 10 sections in the Physics Review Books is a page listing the "Top 10 Section Goals" for that particular section. After reading the text in each section and completing the accompanying MCAT-style passages, we feel that you will have a better conceptual understanding of the material important to the physics found in the Physical Sciences section of the MCAT.

Section I: Translational Motion

Top 10 Section Goals

  1. Understand how to work with units and dimensions. The most widely used system of units in the world is the metric system. Physical measurements consist of counting.

  2. Have a working understanding of the difference between scalar and vector quantities. Physical quantities are classified and manipulated according to whether they are scalars or vectors. Scalar quantities have magnitude only. They have no direction in space. Some examples include time, mass, temperature, electric charge, and chemical concentrations. Vectors are quantities that have both magnitude and direction. Some examples of vector quantities include displacement, velocity, acceleration, force, and torque.

  3. Know how to manipulate vectors. Understand how to add, subtract, and multiply vectors; understand that vector components are independent of one another. Know the difference between a dot (a.k.a. scalar or inner) product and a cross (a.k.a. vector or outer) product. The dot product and the cross product are completely different from one another. Know how to apply the right hand rule to a cross product.

  4. Understand the definitions of the sine, cosine, and tangent functions for a right triangle. A right triangle has a hypotenuse, an angle theta, a side opposite to the angle theta, and a side adjacent to the angle theta. Know that Sin (theta) = opposite/hypotenuse, Cos (theta) = adjacent/hypotenuse, and that Tan (theta) = opposite/adjacent.

  5. Be familiar with the three basic types of motion. Translational motion involves the movement of an object from one place to another. Rotational motion examines how an object rotates about an axis. Vibrational motion examines how an object moves back and forth about some central point or axis. In this section, we will primarily be examining translational motion. In later sections, there will be times when we will discuss the combination of translational motion with both rotational and vibrational motion.

  6. Know the difference between speed, velocity, and acceleration. Speed is defined as distance traveled divided by time. Velocity is the rate of change of displacement. Velocity and speed are often confused with one another. Velocity requires the identification of a direction (vector); speed does not (scalar). The dimensions of velocity are the dimensions of length divided by the dimensions of time. The rate of change of velocity with respect to time is referred to as acceleration. The physical dimensions of acceleration are the units of velocity divided by the units of time.

  7. Understand the concepts behind uniformly accelerated motion in the x-direction. In this section we examine the four equations of uniformly accelerated motion. Memorize them! It is important to keep in mind that these four equations are only valid when the acceleration of an object is constant.

  8. Be able to describe a freely falling body. The average acceleration of gravity near the surface of the earth is about 9.8 m/s2 or 32.2 ft/s2. "Average" is used because very precise measurements of the acceleration of gravity will tell us that it is not exactly the same at all locations on the Earth.

  9. Be able to modify the four equations for uniformly accelerated motion in the x-direction. Assuming the gravitational acceleration is constant, one can modify the equations for uniformly accelerated motion in the x-direction to fit uniformly acceleration motion in the y-direction. Understand why it is common when doing problems with these equations to replace "a" with "-g." Know what the minus sign implies.

  10. Know how to solve problems involving projectiles. Be aware that what takes place in the x-direction and what takes place in the y-direction are two independent and separate quantities. Understand how to quickly separate parts of a given problem into a horizontal component and a vertical component.

Passages and Solutions

Section I includes 10 MCAT-style passages with detailed solutions. Passage topics are centered around information important to translational motion.

Section II: Force and Motion, Gravitation

Top 10 Section Goals

  1. Know the difference between kinematics and dynamics. Kinematics involves the description and analysis of motion without saying what caused it. Dynamics is the study of the forces that are responsible for producing changes in motion. Newton's three laws form the cornerstone of this topic.

  2. Understand Newton's First Law and its applications. An object at rest will remain at rest and an object in motion will continue to move with uniform velocity in a straight line, unless acted upon by an external force. Be aware that this law is not true for all reference frames. In order for this law to be true an inertial reference frame must be established.

  3. Understand Newton's Second Law and its applications. A force acting on an object will give that object an acceleration in the direction of the force. The acceleration of the object is directly proportional to the resultant force applied to the object and inversely proportional to the mass of the object. Quite simply, this law is expressed as F = ma, where force (F) and acceleration (a) have both magnitude and direction--meaning they are vector quantities--while mass (m) is a scalar.

  4. Understand Newton's Third Law and its applications. If one object exerts a force on a second object, the second object will exert a reaction force which is equal in magnitude but opposite in direction on the first object.

  5. Understand the concepts behind frictional forces. The frictional force between one solid and another solid depends on the composition of the two materials, and on how tight the surfaces are being pressed together. Friction tends to oppose the motion of movement of an object. Be familiar with the differences between the static and kinetic coefficients of friction.

  6. Understand how inclined planes work. When considering inclined planes, it is especially important to know how to break forces into components. Know why choosing a coordinate system perpendicular (the y-axis) and parallel (the x-axis) to the plane of the incline is key in solving these types of problems.

  7. Be familiar with the operation of pulleys. Pulleys are systems that are used to change the direction of a given force. A system of multiple pulleys can be used to reduce a force needed to lift a heavy object. Understand the concept of a mechanical advantage.

  8. Understand the concept of uniform circular motion. In order to discuss circular motion, a connection needs to be made between arc length (S), radius (r), and the angle (theta) for motion in a circle. An understanding of the conversion of radians to degrees or degrees back to radians is essential as is the meaning of omega--the angular velocity in radians per second. A firm understanding of uniform circular motion is important, because they are very closely connected with the relations for motion in a straight line.

  9. Be familiar with the concept of centripetal force. A force which is responsible for uniform circular motion is referred to as a centripetal force. In other words, a force that pulls on an object and causes that object to move in a circle is said to exert a centripetal force on that object.

  10. Understand Newton's Law of Gravitation and its applications. Newton's law of gravitation (inverse square law) states that even extremely small pieces of matter in the universe attract each other.

Passages and Solutions

Section II includes 10 MCAT-style passages with detailed solutions. Passage topics are centered around information important to force, motion, and gravitation.

Section III: Work and Energy

Top 10 Section Goals

  1. Know the definition of work. Work is defined as the force exerted on an object as that object undergoes a displacement. The work done by a constant force on an object is just the force times the component of displacement parallel to the direction of the applied force. This is expressed as W = (F)(delta x). Work is a scalar quantity; the units are in joules.

  2. Understand how energy and work are related. Energy is defined as the ability to do work. Know that energy can be classified as either kinetic energy or potential energy.

  3. Understand the relationship between kinetic energy and work. Kinetic energy is the ability of an object to do work because of its motion. Know that the net work done on an object equals the change in the kinetic energy of that object.

  4. Understand the meaning of potential energy. Potential energy is the ability of an object to do work because of its position or configuration. Know that potential energy can only be defined for certain kinds of forces.

  5. Understand the relationship between gravitational potential energy and work. The work done on an object against the gravitational force is defined as the change in the gravitational potential energy of that object. An object has potential energy if that object has some vertical height above a reference height.

  6. Know that gravitational potential energy depends only on the initial and final heights of an object. Gravitational potential energy does not depend on the path an object takes as it moves upwards or downwards.

  7. Realize that potential energy can be stored in an object due to its shape. In this case the classic example is a compressed spring. The energy stored in a compressed spring can be used to do work. This potential energy is missing in a relaxed spring. Understand how to find the amount of work done in compressing a spring.

  8. Know that total energy is conserved. The total energy in the universe is constant. Energy cannot be created nor can it be destroyed, only changed into different forms.

  9. Be familiar with mechanical energy. The mechanical energy represents the total capacity of an object to do work. The mechanical energy is just the sum of the kinetic and potential energies of an object, and is usually given the symbol E.

  10. Be able to define power. Power is the rate of doing work and is expressed in units of watts. Know the simple conversion of watts to horsepower.

Passages and Solutions

Section III includes 10 MCAT-style passages with detailed solutions. Passage topics are centered around information important to work and energy.

Section IV: Equilibrium and Momentum

Top 10 Section Goals

  1. Be familiar with torques. A torque is a measurement of the ability of a force to cause rotation about a given pivot point. Understand the meaning of words or phrases like fulcrum, line of action, and moment (lever) arm.

  2. Be familiar with the equation for calculating torques. Know how to do simple calculations to find the magnitude of the torque about some point.

  3. Know that torques can be represented in terms of a vector product. Be familiar with vector products and their direction in space. Understand why vector C, the vector product of A and B, is perpendicular to both A and B. Be able to determine if vector C points into or out of the plane defined by vectors A and B. Know the right-hand rule. Understand why torques in the counterclockwise direction are taken to be positive while torques in the clockwise direction are taken to be negative.

  4. Be familiar with translational and rotational equilibrium. Know what two conditions must apply for a rigid body to be in both translational and rotational equilibrium.

  5. Know how to be conceptual in analysis of problems involving equilibrium of rigid bodies. If two children of unequal weights are at the ends of a seesaw, then in order for the children to balance on the seesaw, the heavier child must move closer to the pivot point (fulcrum). Be able to intuitively determine how far a child who is twice as heavy as the other child must sit from the pivot point in order to balance the seesaw.

  6. Be familiar with gravitational torques. The force of gravity can produce a torque on an object. To avoid a separate torque calculation caused by the weights of every small part of an extended body, assume that every extended body has a center of gravity. Be able to use this weight force at the center of gravity when analyzing gravitational torques.

  7. Understand the meaning of momentum. Momentum can be thought of as the difficulty experienced in bringing a body to rest. Momentum is a conserved quantity and is related to the motion and mass of a body. The larger the mass of a body and the faster that body moves, the greater its momentum, and the more difficult it is to bring that body to rest.

  8. Understand the meaning of impulse. An impulse is simply a force applied to a body for some given amount of time. An impulse will cause the momentum of a body to change. Be able to analyze simple impulse-momentum problems.

  9. Understand the meaning of a conserved quantity. Examples of conserved quantities are energy, momentum, and electric charge. The amount of these quantities in the universe is believed to never change.

  10. Be familiar with the mathematical expression of linear momentum conservation. Understand why this expression allows one to relate the initial and final velocities of objects before and after their collision without the need to know what the forces are between the objects during their collision.

Passages and Solutions

Section IV includes 10 MCAT-style passages with detailed solutions. Passage topics are centered around information important to equilibrium and momentum.

Section V: Periodic Motion and Wave Characteristics

Top 10 Section Goals

  1. Know the difference between periodic motion and simple harmonic motion. Periodic motion is any motion that repeats itself in a fixed time interval. Examples include the orbital motion of a satellite, the vibration of a guitar string, the swinging of a pendulum. If an object is undergoing a special type of periodic motion called simple harmonic motion, then the acceleration of that object undergoing is proportional to the negative of its displacement. A graph of its displacement as a function of time is that of a sine or cosine function.

  2. Understand the characteristics of simple harmonic motion. This type of motion involves a period, a frequency, and an amplitude. Know how to relate the period to the frequency. Remember that the period is independent of the amplitude.

  3. Have a general understanding of Hooke's law and its applications. The displacement of a spring from equilibrium is proportional to the force acting to displace that spring. This proportionality can be written as F = kx, where k is a force constant that depends on the stiffness of the spring.

  4. Be familiar with the simple harmonic motion of a spring and a pendulum. Understand the similarities and differences between the expression used to calculate the frequency of a vibrating spring and the frequency of a swinging pendulum.

  5. Be able to define a wave. A wave is defined as a transmission of energy through a material. Know that waves carry energy and momentum, but they do not carry mass.

  6. Know what the basic wave characteristics are. All waves have an amplitude, a frequency, a wavelength, a wave speed and they carry energy. Know what the relationship is between these various quantities. Know when the wave frequency of a wave will be constant and when it will change.

  7. Be familiar with the differences between transverse and longitudinal waves. Transverse waves cause vibrations perpendicular to the direction of wave propagation while longitudinal waves cause vibrations parallel to the direction of wave propagation. It is important to understand the relationships between amplitude, frequency, wavelength, and the velocity of waves.

  8. Understand the principle of superposition of waves. This principle says that if two or more waves passing through the same medium meet at a particular point in that medium, then the net displacement of those waves is just the addition of the individual displacements of the waves if they were traveling through the medium alone. Be familiar with constructive and destructive wave interference.

  9. Understand why standing waves do not appear to travel along their line of propagation. Know how to recognize the standing-wave vibration patterns on a string. Understand the meaning of a harmonic, an overtone, a node, and an antinode.

  10. Be familiar with resonance. Understand why the amplitude and hence the energy of the system may increase if one supplies a vibrating force that has a frequency which is the same as the natural frequency of the system.

Passages and Solutions

Section V includes 10 MCAT-style passages with detailed solutions. Passage topics are centered around information important to periodic motion and wave characteristics.

SAMPLE PASSAGE




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