# Comprehensive AP Physics C Syllabus

## Unit 1: Kinematics

 Subtopic Subtopic Number AP Points to understand Kinematics: Motion in One Dimension 1.1 Kinematics is a branch of physics that deals with the motion of objects and their spatial relationships, without taking into account external forces that affect their movement. The kinematic relationships between vector quantities such as position, velocity, and acceleration describe the motion of a particle moving in a straight line. The functions of position, velocity, and acceleration can be used to describe the motion of an object. Position refers to the location of an object in space Velocity refer to the distance covered by an object in unit time Acceleration refers to the rate of change of velocity with respect to time. Kinematics: Motion in Two Dimensions 1.2 Simultaneous relationships between the quantities of position, velocity and acceleration for the motion of a particle moving in a multidimensional without net forces. Calculating vector components in two dimensions Net displacement, net change in velocity, average acceleration vector, velocity vector Vector addition and subtraction Expression for vector position, velocity or acceleration at some point in its trajectory. Calculating kinematic quantities of an object in projectile motion

## Unit 2: Newton’s Laws of Motion

 Subtopic Subtopic Number AP Points to understand Newton’s Laws of Motion: First and Second Law 2.1 Newton’s First Law: An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force. Describing object in a state of equilibrium Calculating acceleration, average force acting on the object, trajectory and net forces on an object in translational motion Newton’s Second Law: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.  Forces acting parallel to a velocity vector have the capacity to change the speed of the object. Forces acting in the perpendicular direction have the capacity to change the velocity vector of the object. Friction is a force that acts against the motion of an object when its surface comes in contact with another surface. Frictional force is the force that arises when two surfaces make contact and slide against each other. Normal force is the force exerted by a surface on any other object that comes into contact with it. Static and kinetic friction refer to two types of frictional forces. Static friction occurs when two or more objects are not moving relative to each other, while kinetic friction arises between two or more objects that are already in motion with respect to each other. Deriving expressions that relate mass, forces, or angles of incline for various slipping conditions with friction Calculating value for static frictional force for an object in dynamic situations Expression for the motion of a free falling object with resistive drag force.  Describing acceleration, velocity, position for an object with a resistive force Terminal Velocity: Maximum speed achieved by an object falling under the influence of a drag force. Circular Motion 2.2 Calculating velocity of an object moving in a horizontal circle with a constant speed. Centripetal acceleration is the acceleration experienced by an object moving along a circular path. Angular velocity is the rate at which an object rotates or revolves around an axis. Uniform circular motion is the motion of an object moving at a constant speed along a circular path, where the velocity changes due to the change in direction. When an object undergoes horizontal circular motion, a force is required to provide the necessary centripetal acceleration, which is always perpendicular to the velocity vector. The critical speed is the minimum speed required at the top of a vertical circle where the gravitational force is the only source of centripetal force. The maximum speed occurs at the bottom of the circle. Newton’s Laws of Motion: Third Law 2.3 Newton’s Third Law: For every action (force) in nature there is an equal and opposite reaction. The forces exerted between objects are equal in magnitude and opposite in direction Deriving expressions that relate acceleration of multiple connected masses moving in a system connected by light strings.

## Unit 3: Work, Energy and Power

 Subtopic Subtopic Number AP Points to understand Work-Energy Theorem 3.1 Work Done: Work is the dot product of Force and the displacement of the object. The component of displacement that is parallel to the applied force is used to calculate the work. Work is a scalar quantity (can be positive, negative or zero) The area under a curve for a force vs position graph equals the work done on the object Net work done on a point like object is equal to the object’s change in the kinetic energy Forces and Potential Energy 3.2 Conservative forces refer to forces that have a constant amount of work regardless of the path taken by the object. In contrast, dissipative forces require varying amounts of work depending on the path taken by the object. If an object moves along a complete closed path, the work done by a conservative force is zero. Examples of dissipative forces include friction, resistive forces, and external forces. Potential energy is the energy that an object possesses due to its position relative to a zero position. This energy is stored and can be released when the object’s position changes. The relationship between potential energy and conservative forces is qualitative and can be represented graphically. Gravitational potential energy is associated with the separation between two objects that attract each other through the force of gravity. Conservation of Energy 3.3 Total Mechanical energy: Describing situations where mechanical energy is either converted to another form of energy or remains constant Conservative system: Systems where no external work is done and the total energy in the system is a constant Application of the conservation of total mechanical energy Exploring the vertical circular motion in the Earth’s gravity Power 3.4 Power: The energy of an object or system can be changed at different rates Calculating amount of power required to maintain constant acceleration.

## Unit 4: Systems of Particles and Linear Momentum

 Subtopic Subtopic Number AP Points to understand Center of Mass 4.1 The displacement, velocity, and acceleration of the center of mass of a system in linear motion can be determined based on the symmetry and regularity of the solid, with the center of mass being located at its geometric center. If the net force acting on an object is zero, its center of mass will not experience any acceleration. The center of gravity is an imaginary point in a body where the total weight of the body is believed to be concentrated, while the center of mass is a position relative to an object or system of objects. Impulse and Momentum 4.2 Impulse refers to the average force exerted on an object over a period of time, as well as the change in momentum experienced by the object. Momentum is a vector quantity defined as the product of an object’s mass and velocity, while total momentum is the vector sum of the momenta of all individual objects in a system. The impulse acting on an object can be determined by calculating the area under a graph of force versus time, and momentum is always conserved in the absence of external forces. Conservation of Linear Momentum, Collisions 4.3 In elastic collisions, kinetic energy is conserved, but in inelastic collisions, kinetic energy is transferred to internal energy. The momentum of the center of mass of a system is not affected by internal forces acting within the system. One-dimensional expressions for the conservation of momentum can be derived for specific collisions.

## Unit 5: Rotation

 Subtopic Subtopic Number AP Points to understand Torque and Rotational Statics 5.1 Torque is a measure of the rotational force exerted on an object around an axis, and it is calculated by multiplying the moment arm by the applied force. To determine the magnitude and direction of torque, one must consider the orientation of the applied force and the position of the axis of rotation. For an object to remain in static equilibrium, two conditions must be met: the net force acting on it must be zero, and the net torque acting on it must also be zero. The moment of inertia is a property of a rigid body that determines the amount of torque required to rotate it around an axis, and it is influenced by the distribution of mass within the body. It can be calculated using calculus. The parallel axis theorem relates the moment of inertia of a rigid body about an axis through its center of mass to the moment of inertia about a parallel axis passing through another point on the body. Rotational Kinematics 5.2 Angular position is measured in radians, which is the ratio of the arc length to the radius of the circular path. Angular displacement is the change in the angular position of an object, and it is defined as the shortest angle between the initial and final positions. Tangential acceleration is the change in the tangential velocity of a point on a rotating object, and it is related to the applied torque and the moment of inertia of the object. Rotational Dynamics and Energy 5.3 When a net torque is applied to a rigid body, it will experience rotational motion around a fixed axis, as governed by Newton’s second law of rotation. A rigid body diagram is a helpful tool for analyzing the rotational motion of a system, as it shows the points of application of the forces acting on the body. Rotational kinetic energy is the energy associated with the rotational motion of an object and is a part of its total kinetic energy. Angular Momentum and its conservation 5.4 When there is no external torque acting on a system, the total angular momentum of the system is conserved, and it can be transferred between objects within the system without changing the total angular momentum. The direction of the angular momentum of a particle is determined by the vector product of its position vector and its linear momentum vector. The conservation of angular momentum applies to rotating systems under certain conditions, such as when the net external torque acting on the system is zero. Calculating change in angular velocity and angular momentum in different situations

## Unit 6: Oscillations

 Subtopic Subtopic Number AP Points to understand Simple Harmonic Motion, Springs, and Pendulums 6.1 Simple Harmonic Motion: A motion in which the restoring force is directly proportional to the displacement of the body from its mean position. Relationship between the phase angle and amplitude in SHM Phase angle or a periodic wave: A wave that repeats as a function of time and position  Describing displacement in relation to time for a mass-spring system in SHM Determining physical characteristics of a spring-mass system from the differential relationship Simple pendulum: A device where its point mass is attached to a light inextensible string and suspended from a fixed support. Potential energy can be calculated using spring constant and displacement from equilibrium of a mass-spring system. Mechanical energy is always conserved in an ideal oscillating spring-mass system. Maximum potential energy occurs at maximum displacement. Velocity and kinetic energy is zero. Describing effects of changing amplitude in a spring-mass system. Total energy of a spring-mass system is proportional to the square of the amplitude.

## Unit 7: Gravitation

 Subtopic Subtopic Number AP Points to understand Gravitational forces 7.1 Newton’s Law of Gravitation: Every object attracts every other object in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance/radius between their centers. Gravitational Acceleration: The object receiving an acceleration due to the force of gravity acting on it.  The gravitational force between two masses is independent of the nature of the masses and depends only on the product of their masses and the distance between them. Gravitational force is proportional to the inverse distance squared. Orbits of Planets and Satellites 7.2 Centripetal force: The gravitational force between the Earth and satellite is the centripetal force of the circular motion. Velocity of a satellite in circular orbit is inversely proportional to the square root of the radius and is independent of its mass. Kepler’s Third Law: The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis Escape speed: Minimum speed required to escape the gravitational field of the planet. The gravitational potential energy is defined to have zero value when it is at an infinite distance away from the planet. Calculating orbital distances and velocities of a satellite in elliptical orbit using angular momentum conservation.

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