Find the coordinates of the center of mass of a right triangle with sides a and b?

Q: A rod of length L has a non – uniform distribution of mass l (x) = A, where A is a constant. Find…

A: The expression for the y-coordinate of center of mass is, The expression for the x-coordinate of…

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

A: The given points are - (0,0) , (2,1) , (0,3) ρ(x,y) = 2(x+y) To find = a) mass                 b)…

Q: Three particles are placed on the vertices of an equilateral triangle of side d = 3.1 cm. The first…

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Q: Two cars collide at an icy intersection and stick together afterward. The first car has a mass of…

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Q: Consider a sheet with density ρ=(x, y) = 2xy2 and occupying the region R= {(x, y )|0 < x < 3, -1 <y…

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Q: Find the center of mass of a thin plate of constant density & covering the region in the first and…

A: Center of mass: The center of mass is defined as the point where the whole mass of a system is…

Q: Find the x coordinate of the center of mass of the bricks shown in the figure

A: From the diagram, And the masses are:

Q: Determine the coordinates where a fourth particle of mass m4 = 30gr will have to be placed in the…

A: m1 = 40 g Coordinates of m1 = (3,1) cm m2 = 20 g Coordinates of m2 = (−2,1) cm m3= 10 g Coordinates…

Q: Consider a rod of length L. The mass per unit length of the rod, p, varies as p = Pos/L, where po is…

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Q: Find the position of the center of mass of a system formed by four particles of masses m1 = m3…

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Q: Problem 9: Three beads are placed along a thin rod. The first bead, of mass m₁ = 22 g, is placed a…

A: m1=22 gm2=11 gm3=43 gd1=1.1 cmd2=1.6 cmd3=4.6 cm

Q: Find the position of the center of mass of a system consisting of three particles with the same mass…

A: Q. Given that Equilateral triangle of sides l with three particles of same mass m at its corners

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

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Q: Find the center of mass of a quarter of a regular circular plate of radius (b).

A: The center of mass of a distribution of mass in space is defined as the unique point where the…

Q: Three point masses 4kg, 2kg and 6 kg lie at (2,-4), (0,2) and (3,-4) respectively. Calculate the…

A: Given The mass at first point is m1=4 kgThe mass at second point is m2= 2kgThe mass at third point…

Q: For the distribution of particles appearing in the plane of the figure, all particles have the same…

A: Solution:

Q: Two cars collide at an icy intersection and stick together afterward. The first car has a mass of…

A:

Q: y(cm) 4. m = 40 g т, 3D 20 g, m, =10 g, -2- 1 -2 2 X(cm) -1 -2- -3 3. 3. 5.

A: m1 = 40 gcoordinates of m1 = (3,1) cmm2 = 20 gcoordinates of m2 = (-2,1) cmm3 = 10 gcoordinates of…

Q: Find the mass and the indicated coordinates of the center of mass of the solid region Q of density p…

A: Given: The equation of the solid region is 3x + 3y + 6z = 18 , x=0, y=0,  z=0 The density of the…

Q: Two cars collide at an icy intersection and stick together afterward. The first car has a mass of…

A: Given data: The mass of the fast car m1=1300 kg The mass of the second car m2=750 kg The velocity of…

Q: Find the position of the center of mass of a bar of homogeneous mass density, length L and cross…

A: Since density is homogenous centre of mass lies at the center of gravity. Which means at half of…

Q: For the distribution of particles appearing in the plane of the figure, all particles have the same…

A: As Given in figure Co-ordinates of Particles of mass m    are (2,3), (9,7), (-2,-6), (-5,5)

Q: A square of side length a = 18.0 cm is placed so its lower-left corner is at the origin of a 2D…

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Q: What are the x and y coordinate of the center of mass relative to the oripgin? angle, as show…

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Q: A stone is dropped at t = 0. A second stone, with 3 times the mass of the first, is dropped from the…

A: Let first stone have mass=m1 and second stone have mass=m2 We have,m2=3m1

Q: Find the center of mass of a unit hemisphere if the density at a point is proportional to the square…

A: We are considering a solid hemisphere of mass M and has the radius R. The centre of mass will…

Q: A tabletop gamer has designed a game that requires three dice to be thrown onto a tray with a…

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Q: help please  If a 10 kg bowling ball, moving at 8 m/s to the right, hits and bounces off a second…

A: Given, The mass of the ball, m1 = 10 kgmoving with speed, u1 = 8 ms   (rigjt)mass of the second…

Q: Find the y center of mass of the following masses at their respective coordinates: m1=5.0,…

A: solution as

Q: Find the center of mass of the given system of point masses lying on the x-axis. m, = 0.2, m, = 0.2,…

A: Given that---- m1 = 0.2 , m2 = 0.2 , m3 = 0.3 , m3 = 0.2 x1 = 1 , x2 = 2 , x3 = 3 , x4 = 4 Question…

Q: Three particles of masses m1 = 2.5 kg, m2 = 4.1 kg and m3 = 3.1kg are at the corners of an…

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Q: Find the center of mass of the thin half-disk whose region is bounded above by the semicircle and…

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Q: Find the y center of mass of the following masses at their respective coordinates: m1=5.0,…

A: Given:

Q: The position of masses 3kg, 4kg, 6kg and 10kg are (0,1) (5,2), (0,5) and (5,7) respectively.…

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Q: Two cars collide at an icy intersection and stick together afterward. The first car has a mass of…

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Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).