Relative motion is the concept of describing how an object's position or velocity changes from the perspective of another moving object or a specific frame of reference. Motion is not absolute; it is always relative to an observer's chosen point of reference, which can be a stationary point or another moving object. For example, a person walking on a moving train is stationary relative to someone on the train but appears to be moving relative to someone standing on the ground outside the train. 💡Key concepts • Frame of reference: A coordinate system or point of view used to measure motion. The concept of relative motion is about how a change in position is measured from different frames of reference. • Relative velocity: The velocity of an object as measured by an observer in a different reference frame. This can be calculated by finding the difference between the velocities of the two objects relative to a third, common reference frame. • Vector quantities: Velocity and displacement are vector quantities, meaning they have both magnitude and direction. When calculating relative motion, these vector directions must be considered, often using vector diagrams or equations. • Example: Imagine a car moving at \(60\) mph and a person walking inside it at \(5\) mph in the opposite direction of the car's travel. The person's velocity relative to the ground is \(55\) mph, while their velocity relative to the car is \(5\) mph in the opposite direction. 💡Worksheets are provided in PDF format to further improve your understanding: • Questions Worksheet: https://drive.google.com/file/d/1FZHK2lvewIfauVNmVxQprxLvhBZfVv02/view?usp=drive_link • Answers: https://drive.google.com/file/d/1h8pFAHvhQo5qqSPsfYA9GETrdjMQg8z8/view?usp=drive_link 💡Chapters: 0:00 Reference frames and relative motion 3:45 Worked examples 🔔Don’t forget to Like, Share & Subscribe for more easy-to-follow Calculus tutorials. 🔔Subscribe: https://rumble.com/user/drofeng _______________________ ⏩Playlist Link: https://rumble.com/playlists/d3cTgspk0Ro _______________________ 💥 Follow us on Social Media 💥 🎵TikTok: https://www.tiktok.com/@drofeng?lang=en 𝕏: https://x.com/DrOfEng 🥊: https://youtube.com/@drofeng

This AP Physics C (Mechanics) video defines the vector dot product. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video explains how a vector can be represented in a Cartesian coordinate system using the vector dot product. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video provides a proof of the vector dot product in a 2D Cartesian coordinate system. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the work done by a force using the vector dot product. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the work done by a force to displace a particle along a curved path using the vector dot product. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers a worked example on the work done by a force acting on a particle. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the work-energy theorem and kinetic energy. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers a worked example on the work-energy theorem. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the gravitational potential energy stored in a particle near the surface of the Earth. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the elastic potential energy stored in a spring in a spring-mass system. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines conservative forces and demonstrates how the work done by these forces is path independent. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines dissipative forces and demonstrates how the work done by these forces is path dependent. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the relationship between a conservative force and potential energy function. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers worked examples on potential energy functions. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the conservation of mechanical energy. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines conservative systems. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video demonstrates a problem where both energy and force analysis need to be applied to solve for unknown physical characteristics in the system. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers worked examples on the conservation of mechanical energy. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines power as the rate of the work done by a force, and also explains horsepower. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers worked examples on power. This video is part of Unit 3 of AP Physics C (Mechanics) on Work, Energy and Power. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the center of mass of a discrete body. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video defines the center of mass of a continuous body. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video explains the difference between the center of mass and center of gravity. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers a worked example on finding the center of mass of a system of particles. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video covers a worked example on finding the center of mass of a continuous body. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video derives the equation of motion for a system of particles. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video derives the impulse-momentum equation from Newton's second law of motion. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This AP Physics C (Mechanics) video derives the impulse-momentum equation for a system of particles from Newton's second law of motion. This video is part of Unit 4 of AP Physics C (Mechanics) on Systems of Particles and Linear Momentum. You can contact me through the comments and community section, or email me at [email protected] for questions.

This physics video covers a tutorial on using the mean value theorem for integrals to obtain an equivalent definition of an impulse using the average force. The impulse is a force applied over a time interval. Geometrically, the impulse is the area under the force vs time curve. Hence, different equivalent forms of the impulse can be used in the impulse momentum theorem depending on the physics problem being analysed.

This physics video demonstrates how to apply the impulse and momentum theorem to a physics problem. It gives a geometric interpretation of the impulse, which is a force applied over a time interval. An example of an explosion on a spring mass system is used to demonstrate how the impulse and momentum theorem can be used along with the conservation of energy to solve for the deformation of the spring.

This physics video covers a tutorial on the conservation of momentum for a system of particles. It explains when momentum is conserved and when it is not. Generally, momentum is conserved when there is no net external force acting on the system. The conservation of momentum is commonly applied to solve for the velocities of particles involved in in elastic and inelastic collisions. Note that the internal forces in the system cancel each other out by Newton's third law, so momentum is not conserved for a single particle subjected to an impulse.

This physics video covers a tutorial on the conservation of momentum for a system of particles in 2D Cartesian coordinates. It explains when momentum is conserved and when it is not. Generally, momentum is conserved when there is no net external force acting on the system. The conservation of momentum is commonly applied to solve for the velocities of particles involved in in elastic and inelastic collisions. Note that the internal forces in the system cancel each other out by Newton's third law, so momentum is not conserved for a single particle subjected to an impulse.

This physics video covers a tutorial on the conservation of momentum applied to elastic collisions. Both momentum and kinetic energy are conserved for a system of particles undergoing elastic collisions with no external forces acting on the system.

This physics video covers a tutorial on the conservation of momentum applied to inelastic collisions. Momentum is conserved for a system of particles undergoing inelastic collisions with no external forces acting on the system but kinetic energy is not conserved. In a perfectly inelastic collision both masses are connected and have the same velocity after the collision occurs.

This physics video covers a tutorial on the conservation of momentum applied to elastic and inelastic collisions. Worked examples on elastic and inelastic collisions are provided to reinforce your understanding on the conservation of momentum.

This physics video covers a tutorial on the vector cross product. The vector cross product returns a vector whereas the vector dot product returns a scalar. A geometric interpretation of the cross product is given. The vector cross product is used in physics applications to determine quantities such as torque, angular velocity, angular acceleration and angular momentum.

This physics video covers a tutorial on the vector cross product and how to visualise it using the right hand rule. It shows that the vector cross product is not commutative.

This physics video covers a tutorial on the vector cross product and how to calculate it using the determinant of a matrix.

This physics video covers a tutorial on the proof of the vector cross product in 2D Cartesian coordinates. The vector cross product is useful in calculating physical quantities such as torque, angular momentum, angular velocity and angular acceleration.

This physics video covers a tutorial on the vector cross product using a worked example to reinforce your understanding. The tangential velocity is calculated from the cross product between the angular velocity and radial vectors seen in circular motion.

This physics video covers a tutorial on torque or moment of a force using the vector cross product.

This physics video covers a tutorial on torque or moment of a force using the moment arm, which is the perpendicular distance from a pivot point to the line of action of a force. Using the moment arm simplies the calculation of a torque.

This physics video covers a tutorial on the equilibrium of an extended rigid body. For a rigid body to be in equilibrium, both the net force and net torque acting on the body must be zero.

This physics video covers a tutorial on the equilibrium of an extended rigid body. For a rigid body to be in equilibrium, both the net force and net torque acting on the body must be zero. A worked example is covered to enhance your understanding.

This physics video covers a tutorial on the moment of inertia of a system of particles. Similar to mass resisting a force, the moment of inertia resists a torque.

This physics video covers a tutorial on the moment of inertia of a rigid body. Similar to mass resisting a force, the moment of inertia resists a torque.

This physics video covers a tutorial on the moment of inertia of a system of particles. Similar to mass resisting a force, the moment of inertia resists a torque. A worked example is provided to reinforce your understanding.

This physics video covers a tutorial on the moment of inertia of a rigid body. Similar to mass resisting a force, the moment of inertia resists a torque. Worked examples on the moment of inertia of a thin rod, thin ring, thin disc, annular ring and cylinder are provided to reinforce your understanding.

This physics video covers a tutorial on the parallel axis theorem, which is used to find the moment of inertia of a rigid body about an arbitrary axis using the moment of inertia about the center of mass.

This physics video covers a tutorial on the parallel axis theorem, which is used to find the moment of inertia of a rigid body about an arbitrary axis using the moment of inertia about the center of mass. Worked examples are provided for practice.

This physics video covers a tutorial on the rotational kinematics of a rigid body. It demonstrates the relationships between the tangential and angular velocities and accelerations.

This physics video covers a tutorial on the big five kinematic equations for rotational the motion of a rigid body. Similar to translational motion, these apply when the angular acceleration of the rigid body is uniform.

This physics video covers a tutorial on the rotational kinematics of a rigid body, including the big five rotational kinematic equations. Worked examples are covered to enhance your understanding. 0:00 Worked example, angular and tangent velocities 1:35 Worked example, uniform angular acceleration 3:07 Worked example, non-uniform angular acceleration

This physics video covers a tutorial on the kinematics on rolling motion with no slip.

This physics video covers a tutorial on rotational dynamics. 0:00 Rotational analog of Newton's second law 1:52 Rigid body diagrams 3:08 Worked example on Newton's second law and rotation about a fixed axis 4:11 Worked example on Newton's second law with free rigid body motion 6:01 Newton's second law applied to rolling motion with no slip 8:08 Worked example on Newton's second law for rotation applied to a cable pulley system 10:31 Worked example on rolling motion with no slip 12:01 Rotational kinetic energy for a rigid body under fixed axis rotation 13:02 Rotational kinetic energy for a rigid body under 2D planar motion 14:28 Worked example on rotational work and kinetic energy 16:11 Worked example on rotational work and kinetic energy 17:39 Conservation of energy for rolling motion with no slip 19:23 Worked example on the conservation of energy for rolling motion with no slip 21:18 Worked example on the conservation of energy for system undergoing translation and rotation

This physics video covers a tutorial on angular momentum and the conservation of angular momentum. 0:00 Spin angular momentum about a fixed axis 1:09 Definitions of angular impulse 2:18 Orbital angular momentum of a particle 4:23 Worked example on angular impulse and momentum about a fixed axis 6:01 Worked example on angular impulse and momentum about the center of mass of a rigid body 7:07 Conservation of angular momentum for a rigid body 9:19 Conservation of angular momentum for a system of particles and rigid bodies 11:57 Worked example on the conservation of angular momentum

This physics video covers a tutorial on oscillations with a focus on simple harmonic motion. 0:00 Simple harmonic motion, Newton's second law, differential equation 1:33 Solution to differential equation 2:47 Amplitude, period, frequency 4:43 Phase lag 6:24 Initial conditions 7:47 Worked example on simple harmonic motion 9:13 Kinematic characteristics 11:27 Vertical oscillator 13:19 Oscillators with springs in series and in parallel 18:41 Simple, physical and torsional pendulums 23:50 Conservation of energy for different oscillators 29:14 Worked examples on oscillation 37:41 Interpreting experimental data for a pendulum

This physics video covers a tutorial on deriving the solutions to the ordinary differential equation describing simple harmonic motion. 0:00 Derivation of the solution to the ODE 1:29 Alternate solution using Euler's formula 3:00 Alternate solution using trig identities

This physics video covers a tutorial on gravitational forces. 0:00 Newton's law of gravitation 2:00 Gravitational acceleration near the Earth's surface 3:21 Gravitational forces of extended bodies 5:37 Worked example on gravitational forces

This physics video covers a tutorial on Kepler's laws for planetary and satellite orbits. 0:00 Kepler's laws of motion 1:57 Satellite orbits, geosynchronous orbit 4:49 Worked examples on Kepler's laws and satellite orbits 8:44 Verifying Kepler's third law using experimental data

This physics video covers a tutorial on gravitational potential energy, energy of satellite orbits and escape speed. 0:00 Gravitational potential energy 2:21 Gravitational potential energy, reference at infinity 3:28 Kinetic energy of a satellite orbit 5:01 Total mechanical energy of a satellite orbit 5:56 Escape speed 7:17 Worked example on gravitation below the earth's surface