Linear refers to something that is straight or follows a straight line. In mathematics, a linear function is a function that has a constant rate of change, meaning that as the input variable increases by a fixed amount, the output variable also increases by a fixed amount. The graph of a linear function is a…
Resonance is a phenomenon that occurs when a system or object is subjected to a periodic disturbance, such as a sound wave or a vibration, that has the same frequency as the natural frequency of the system or object. When this happens, the system or object responds with an increased amplitude of oscillation. For example,…
Damped oscillation refers to the behavior of a system that undergoes oscillation (i.e., periodic motion) but with the amplitude of the oscillation decreasing over time due to the presence of damping. In one dimension, a simple example of a damped oscillation is a mass-spring system with damping, where a mass is attached to a spring…
“Mechanics forced” could refer to a few different things depending on the context, but one possible interpretation is the concept of forced motion in mechanics. Forced motion in mechanics refers to a system that is subject to external forces that cause it to move in a specific way, rather than moving according to its own…
When a point mass collides with a rigid body, the collision can be classified as either elastic or inelastic. In an elastic collision, the total kinetic energy of the system is conserved. That is, the kinetic energy of the point mass and the rigid body before the collision is equal to the kinetic energy of…
The equilibrium of rigid bodies refers to the state of a rigid body when it is at rest or moving with a constant velocity, and the net force and torque acting on it are both zero. In other words, the body is not accelerating and is in a state of balance. To determine the equilibrium…
Cylinders and spheres are both three-dimensional shapes commonly encountered in mathematics and the physical world. Here are some important characteristics of each shape: Cylinder: Spheres: Both cylinders and spheres have properties that make them useful in a variety of applications. For example, cylinders are commonly used as containers for liquids or gases because they have…
When a ring rolls without slipping, it means that the ring is rotating around its axis while also translating without any slipping on a surface. In this situation, the point on the ring’s edge that is in contact with the surface has zero velocity relative to the surface, while the ring’s center of mass is…
The dynamics of rigid bodies with a fixed axis of rotation can be described using rotational motion equations and principles. Firstly, it’s important to note that for a rigid body rotating about a fixed axis, all particles of the body rotate in circles or arcs about the axis, with the same angular velocity. The rotational…
Conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a system is conserved in the absence of external torques. Angular momentum is a property of rotating objects and is defined as the product of the moment of inertia and the angular velocity. In simpler terms, the…
