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Chapter 9
Center of Gravity and Centroid

Center of Gravity
The center of gravity is the point at which an object's weight appears to be concentrated and can be used to balance the object perfectly. This…
Center of Mass
The center of mass is the point at which the total mass of an object can be said to be concentrated. It is a fundamental principle in mechanics and…
Centroid of a Body
The centroid is an important concept in engineering, physics, and mechanics. It is the geometric center of a body. It always lies within the body…
Centroid of a Body: Problem Solving
The centroid of a body is a crucial concept in engineering and physics. Finding the centroid of a body can help determine its stability, its balance…
Centroid for the Paraboloid of Revolution
The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in…
Composite Bodies
A composite body is a body made up of multiple parts, connected to form a larger, unified object. Each part has its own weight and center of gravity,…
Theorems of Pappus and Guldinus
The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any…
Theorems of Pappus and Guldinus: Problem Solving
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes.…
Resultant of a General Distributed Loading
While designing structures exposed to non-uniform loads, it is crucial to consider the resultant force and its location. This resultant force is a…
Fluid Pressure
In mechanical engineering, fluid pressure plays a critical role in designing systems that utilize liquid flow, such as hydraulic systems, pumps, and…
Fluid Pressure over Flat Plate of Constant Width
When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design…
Fluid Pressure over Curved Plate of Constant Width
When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and…
Fluid Pressure over Flat Plate of Variable Width
When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag…
Postural Organization of Gait Initiation for Biomechanical Analysis Using Force Platform Recordings
Gait initiation (GI), the transient phase between orthograde posture and steady-state locomotion, is a functional task and an experimental paradigm…
A Microfluidic-based Hydrodynamic Trap for Single Particles
The ability to confine and manipulate single particles in free solution is a key enabling technology for fundamental and applied science. Methods…
A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
The center of resistance (CRES) is regarded as the fundamental reference point for predictable tooth movement. The methods used to estimate the CRES…

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