The law of gravitation, also known as Newton’s law of gravitation, is a fundamental principle in physics that describes the force of attraction between two objects with mass. The law states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their…
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…
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…
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…
Angular momentum is a fundamental concept in physics that describes the rotational motion of an object or system. It is a vector quantity that has both magnitude and direction, and is defined as the product of the moment of inertia of the object and its angular velocity. The moment of inertia is a measure of…
The moment of inertia of a uniform body with a simple geometrical shape depends on the distribution of mass within the body and the shape of the body itself. Here are some common examples: I = (1/12)ML^2 I = (1/2)MR^2 I = (1/2)M(R2^2 + R1^2) I = (2/5)MR^2 I = (2/3)M(R2^3 – R1^3)/(R2 – R1)…
The perpendicular axes theorems are a set of rules used in the study of moments of inertia, which are physical properties of objects that describe how difficult they are to rotate around various axes. The perpendicular axes theorems state the following: These theorems are very useful in determining moments of inertia for objects with complicated…
A rigid body is an idealized object in classical mechanics that does not deform under external forces. It is a theoretical concept that assumes that an object is perfectly solid and does not change its shape or size when subjected to external forces. In reality, no object is truly rigid, but many objects can be…
