Centroids in planar lamina 4
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This document discusses centroids and moments for planar lamina. It defines a centroid as the center of mass of an object of uniform density. Centroids have certain characteristics, such as lying on any line of symmetry. The document presents equations to calculate the mass, moments, and centroid of a planar lamina bounded by functions f(x) and g(x). It provides an example of finding the centroid of a region bounded by f(x)=x and g(x)=x4, with the centroid being (0.56, 0.37). Real life applications include balancing objects and hanging items on a wall.
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Simple harmonic motion (SHM) describes the motion of an object undergoing displacement from an equilibrium position due to a restoring force proportional to the displacement. The motion is periodic and sinusoidal, with the displacement following the equation x=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase. Examples of SHM include a mass attached to a spring and the pendular motion of a mass hanging from a fixed point by a string.
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Motion in a Straight Line Class 11 Physics
As students embark on the journey into the fascinating realm of physics in Class 11, one of the fundamental topics that captivates their attention is "Motion in a Straight Line." This foundational concept forms the bedrock of kinematics, the branch of physics concerned with the description of motion. In this chapter, students explore the dynamics of objects moving along a linear path, unraveling the principles that govern their displacement, velocity, and acceleration. From understanding the basic distinctions between scalar and vector quantities to delving into the equations that quantify motion, Class 11 students embark on a captivating exploration of the fundamental laws that underpin the linear journey of objects in motion. Motion in a straight line not only serves as a gateway to more intricate concepts in physics but also provides a lens through which students perceive and analyze the dynamics of the world around them.
For more information, visit. www.vavaclasses.com
5 volumes and solids of revolution i x
The document discusses solids of revolution and calculating their volumes. It explains that for a solid obtained by rotating a region bounded by a function y=f(x) around the x-axis from x=a to x=b, the cross-sections are circular discs with radius f(x). Therefore, the cross-sectional area is π[f(x)]2 and the volume can be calculated as the integral from a to b of π[f(x)]2 dx.
Vibration advance longi and trans equation.
1. A longitudinal disturbance along a stretched string or bar can propagate as a wave.
2. The wave equation derived to describe this propagation is analogous to the wave equation for transverse waves on a string.
3. The speed of the longitudinal wave is determined by the Young's modulus and linear density of the material, similar to the speed of transverse waves on a string.
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Physics
1. The document discusses various topics in waves, optics, oscillation, and gravitation including traveling waves, standing waves, wave propagation, simple harmonic motion, Newton's laws of gravity, and key terms.
2. Examples are provided to demonstrate calculations for spring oscillation, wave speed in a string, pendulum motion, and gravitational acceleration based on pendulum period.
3. Formulas are listed for spring constant, frequency, wave velocity, and other important relationships.
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1. The document discusses various topics related to waves, optics, oscillation, and gravitation. It defines key terms like traveling waves, standing waves, and wave propagation.
2. Important concepts are covered, including the principle of superposition, simple harmonic motion, Newton's laws of gravitation, and Kepler's laws of planetary motion.
3. Examples are provided to demonstrate applications of these concepts, such as calculating spring oscillation properties and determining values related to a vibrating string and pendulum motion.
3. Motion in straight line 1.pptx
1. The document discusses motion in a straight line, including key concepts like displacement, average and instantaneous velocity, acceleration, position-time and velocity-time graphs.
2. It provides equations for uniformly accelerated motion relating position, velocity, time, and acceleration.
3. Examples of relative motion and relative velocity between two objects moving with different average velocities along the same axis are given.
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Centroids in planar lamina 4
- 1. Centroids in a Planar Lamina Young Lee Brian Lau Alvin Lau Jonathan Javier
- 2. Introduction to Centroids Centroid (Center of gravity) The center of mass of an object of uniform density Characteristics of a centroid If a region has a line of symmetry, then its centroid is on that line of symmetry If a region has two lines of symmetry, then the centroid is the point where they intersect Moment A measure of tendency to cause a body to rotate about a specific point No movement at the center of gravity Planar Lamina A thin and flat plate of material of constant density Density (𝝆): measure of mass per unit of area
- 3. Illustration f(x) R g(x) a b
- 4. Illustration Mass of Planar Lamina (R)
- 5. Illustration f(x) 𝜟x R f(x) — g(x) Subinterval, mi g(x) a b
- 6. Illustration Mass of subinterval
- 7. Illustration f(x) 𝜟x R f(x) — g(x) g(x) a b
- 8. Illustration Moment of mi about the x-axis Moment of mi about the y-axis
- 9. Centroidal Equations Mass of lamina: Moment of planar lamina about the x-axis: Moment of planar lamina about the y-axis: Center of Mass:
- 10. Example Find the centroid of the region bounded by the graphs f(x) = x and g(x) = x4 Centroid: (0.56, 0.37)
- 11. Real Life Application Balancing objects with uniform density Hanging objects on a wall