Circular motion: Concepts and Calculations

This lecture covers the fundamental concepts of circular motion, including centripetal acceleration, centripetal force, and the relationship between velocity and acceleration in polar, cylindrical, and spherical coordinate systems. It also delves into the importance of friction in auto racing and the physics behind Formula 1 tire width. The instructor explains how to derive expressions for velocity and acceleration in cylindrical coordinates, as well as the cross product and its applications in circular motion. The lecture concludes with a summary of uniform circular motion and a demonstration of a ball on a rotating slide.

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PHYS-101(en): General physics : mechanics (English)

Students will learn the principles of mechanics to enable a better understanding of physical phenomena, such as the kinematics and dyamics of point masses and solid bodies. Students will acquire the c

Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.

Acceleration

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes: the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.

Center of mass

In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion.

Del in cylindrical and spherical coordinates

This is a list of some vector calculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The polar angle is denoted by : it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by : it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.

Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.

Coordinate Systems: Polar, Cylindrical, Spherical PHYS-101(a): General physics : mechanics

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Polar Coordinates: Position and Velocity PHYS-101(a): General physics : mechanics

Explores polar coordinates, position, velocity, and acceleration vectors in Cartesian and polar systems, including cylindrical and spherical coordinates.

Circular motion: Friction and Newton's Laws PHYS-101(en): General physics : mechanics (English)

Explores circular motion, friction, and Newton's laws in various coordinate systems.

Physics 1: Harmonic Oscillator and Spherical Coordinates PHYS-101(g): General physics : mechanics

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Linear Momentum Conservation and Stress in Continuum

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.