## Calculus Based Physics I...YouTube Videos: Calculus Review, Motion, Vectors, Newton's Laws, Conservation Laws, Thermodynamics, Waves

Sections on this page:
[UNIT 1: Functions, Graphs, Slope, Derivative, Kinematic Equations ]
[UNIT 2: Work and KE, Rocket Motion, Rotational Inertia]
[UNIT 3: ]
[UNIT 4: ]
[UNIT 5: ]

 Unit 1 Functions, Graphs, Slope, Derivative, Kinematic Equations Function, Graph, Slope, Linear and Quadratic Functions Concept and Example (17 minutes) This is the first video in a series of videos designed to help a student enrolled in a physics course that uses calculus. This video describes function notation, how to evaluate a function, how to graph a function, and how to find slope for a function. Derivative of Linear and Quadratic Functions and Slope Concept and Example (13 minutes) This is the second in a series of videos for a student enrolled in a calculus based physics course. This video introduces the derivative operation and how it can be used to determine the slope of a function. A linear function and a quadratic function are used. The same functions were used in the first video of this series and non-calculus methods were used to find the slope. Derivative of a Function, Slope, Examples Examples (7 minutes) This video has two examples where the derivative of the function is determined. For both cases the slope of the function is determined at a certain value of the independent variable and the location where the slope is zero is determined. Calculus Review, Antiderivative, Area Under Curve Concept (12 minutes) This video gives a quick explanation of how to use the antiderivative (integration) operation. The video calculates the area under a linear function graph and under a parabolic graph. ...................................... Kinematic Equations, Antiderivative Example (6 minutes) New 2016 This video starts with the assumption that the acceleration value is constant. The antiderivative operation is used to develop the velocity equation and then the position equation. Derivative and Kinematic Equations Example (6 minutes) This video assumes the kinematic equation that relates position, initial velocity, time, and acceleration is given. The derivative operation is applied twice to develop the equation for final velocity and deduce the nature of the acceleration. Vectors, Unit Vectors, Dot and Cross Products Concept (15 minutes) This video describes the i,j,k unit vectors and how they can be used to describe a vector. The video shows how to find the x and y components of a vector. The video evaluates the Scalar, or Dot, Product in two ways. The video evaluates the Vector, or Cross, Product in two ways. The direction of the vector result is obtained with the Right Hand Rule ...................................... Derivation of Final Velocity of a Rocket Example (12 minutes) The tools of calculus are used to derive the formula for the final velocity of a rocket in terms of the intial velocity, exhaust velocity of the fuel, and the initial and final masses of the rocket. F=ma cannot be used. It is assumed there is no star or planet near the rocket Derivation of the Relation of Work and Change in Kinetic Energy Example (5 minutes) This video uses the tools of calculus to derive the relationship between work done on an object and the change in the kinetic energy of the object. It is assumed that the mass of the object is constant and there is no change in the potential energy of the object. Calculate Work Done by Variable Force and Final Velocity Example (4 minutes) The tools of calculus are used to determine the amount of work done by a variable force over a given displacement. The final velocity of the object is also calculated. Work Done By A Spring, Calculus Method Example (9 minutes) The work done by a spring is calculated using the antiderivative. The force a spring applies to an object is a variable force so the kinematic equations cannot be used. After the work is calculated the value is compared to the change in potential energy of the spring and the velocity of the object is calculated ...................................... Derivation of Formula for Gravitational Potential Energy Concept (10 minutes) This video uses the tools of calculus to derive the correct formula for gravitational potential energy. The PE of the Earth-Sun system is calculated Total Energy for a Circular Orbit, Planets and Hubble Telescope Example (12 minutes) This video discusses the total energy for an orbit (KE + PE). PE is taken to be zero when the objects are separated by an infinite distance. The total energy for the orbits of Venus, Earth, Mars, and the Hubble Telescope are calculated. The video discusses that if the total energy is negative the object is in a "bound" orbit and will not leave the central body. Gravitational PE, Value of h Where mgh Has Error of 10 Percent Concept (8 minutes) mgh is often used to calculate the change in gravitational potential energy. This video calculates the value of h at which mgh is in error by 10% compared to the correct calculation GM1M2/R. Calculus Derivation of Centripetal Acceleration Concept (11 minutes) The tools of calculus can be ussed to derive the direction and magnitude of centripetal acceleration. The radius vector is written in terms of cosine and sine functions. The derivative is taken twice to produce the acceleration vector. The acceleration vector and radius vector are compared to determine the direction of the centripetal acceleration. V=R w is used to produce the formula for centripetal acceleration. ...................................... Precession of Toy Top and Application to Earth Concept (9 minutes) The weight of a toy top creates a torque that causes the rotation axis of the top to move. The vector nature of torque and angular momentum are discussed. The precessioin of the Earth's rotation axis is discussed. The "Pole Stars" Polaris and Thuban are discussed along with Egyptian pyramids. Precession of Bicycle Wheel Concept (7 minutes) This video describes the unusual motion of a rotating bicycle wheel that is only supported on one end of its axis. The vector nature of torque and angular momentum are described. The motion of the rotation axis is known as precession. . Return to the top of this page. ... OR ... Return to physics.gpclements.com
 Unit 2 Rotational Inertia Derivation of Rotational Inertia Formula for Sphere Concept (11 minutes) This video uses the tools of Calculus to derive the formula for the rotational inertia of a solid sphere that has uniform density. Derivation Formula for Rotational Inertia for Hollow Cylinder Concept (9 minutes) This video uses the tools of calculus to derive the formula for the rotational inertia (moment of inertia) for a hollow cylinder. Derivation of Formula for Rotational Inertia of a Rod Concept (5 minutes) This video uses the tools of calculus to derive the formula for the rotational inertia for a horizontal rod that is rotating about a vertical axis at one end of the rod. ...................................... ...................................... ... Return to the top of this page. ... OR ... Return to physics.gpclements.com
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