The length of a rod is 9 inches and the linear density of the rod at a point x inches from one end is (4x+1) slugs/inches.    Find the total mass and the center of mass.

Q: The figure below shows four particles at the comers of a rectangle, connected by rods of negligible…

A: (a) From the figure, the distance of the masses from the x axis is 3.0m. then the moment of inertia…

Q: A 6 meter rod has a linear density of f(x) = ax + b, if one one end the linear density is 2kg/m and…

A: Given data The length of the rod is l = 6 m The relation of the linear density is f (x) = ax + b The…

Q: Explain how the condition (sum)F = 0 is satisfied for the meter stick in case 1 of the experiment.…

A: Given information:Mass of the block (m1) = 100 g = 0.1 kgMass of the block (m2) = 200 g = 0.2 kgLet…

Q: How could the center of mass be affected if a spherical object has a greater density of mass on one…

A: The point where the total mass of an object is believed to be concentrated is called the center of…

Q: our bricks of length L, identical and uniform, are stacked on top of one another (the figure) in…

A: Given:- Four bricks of length L, identical and uniform, are stacked on top of one another (the…

Q: Two bodies of masses 5 kg and 10 kg are moving towards each other with equal velocities of 15 m/sec.…

A: Let, the body of mass m1=5 kg to left with velocity 15 m/s v1=-15 m/s and the body of mass m2=10 kg…

Q: The center of mass (or center of gravity) of a two-particle system is at the origin. One particle is…

A: Center of mass lies on Origin (0,0) m1=2Kg m2=3Kg

Q: 5. Find the single mass M which can replace the system below and Determine its distance from the…

A: Total moment around O is  Moment=(10*2)+(5*4)+(5*7)=20+20+35=75 Nm

Q: A 4-kg particle has a velocity of (i-5j) m/s , and a 3-kg particle has a velocity of (2i+j) m/s What…

A: Given values: Mass, m1=4 kg Mass, m2=3 kg Velocity, v1→=i^-5 j^ m/s Velocity, v2→=2 i^+j^ m/s

Q: For which kind of bodies made of the same material is the lumped system analysis more likely to be…

A:

Q: An arrow of mass 0.0025 kg is shot from a bow. If the string is stretched a distance m using a force…

A:

Q: Calculate the magnitude of the linear momentum of a 53.8 kg object on the equator as measured from…

A: The magnitude of linear momentum of 53.8 kg objects can be calculated using following steps:Given:

Q: A sphere A of mass m=2 kg is released from rest in the position shown and strikes the frictionless…

A: Draw the diagram of the problem.

Q: A space vehicle is traveling at 4150 km/h relative to the Earth when the exhausted rocket motor is…

A:

Q: A 2.0 m rod of negligible mass connects two small objects. The mass of one object is 1 kg and the…

A: SOlution: given that mas of first object m1 = 1 kg distance between two mass is = 2 m centre of mass…

Q: Two particles with masses in the ratio 1 : 9 are moving with equal kinetic energies. The magnitude…

A: Given data:  m1/m2 = 1/9 The kinetic energies of particles are equal KE1 = KE2 Required: The ratio…

Q: In an elastic collision experiment, the trace pattern of the discs of mass m, and m, was observed as…

A:

Q: If the resultant of all the external forces acting on a system of particles is zero, then from an…

A: Option (a) is correct.

Q: A rocket takes off from an asteroid and reaches a speed of 100 m/s. You may neglect the…

A:

Q: The given masses m¡ are located at the given points Pi which are placed in the xy-plane. Find the…

A: Given that,m1=3 kgm2=8 kgx1,y1=-1,1x2,y2=2,-1x3, y3=3,2

Q: A bullet of mass 4.3 g strikes a ballistic pendulum of mass 3.4 kg. The center of mass of the…

A: Given in the question, Mass of the bullet, mb=4.3 g, Mass of the pendulum mp=3.4 kg and height h=9.3…

Q: The rocket takes off from Earth and reaches a speed of 130 m/s in 13.0 s. If the exhaust speed is…

A:

Q: The center of gravity coincides with the center of mass: O if the body has a uniform distribution of…

A: Center of mass is the point where whole mass of the body is supposed to be concentrated. Center of…

Q: Calculate the velocity of a moving body of mass 5kg whose linear momentum is 2.5kg m/s.

A: Given data :        Mass = m       Momentum = M        To find :           Velocity

Q: An astronaut floating at rest in space has run out of fuel in her jetpack. She realizes that…

A:

Q: Find the center of mass for the particle system with 6 identical masses (x, y in meter)

A: If there are large number of mass m 1,m2,m3.......mn situated at points having coordinates (x1,y1),…

Q: What is the linear momentum of a 74.0 kg object on the Equator, as measured from the center of…

A: Given that:m=74.0 kgR=6371 km

Q: Consider a system of two identical particles. One of the particle is at rest and other has an…

A: We know thatCentre of mass acceleration is given byacom=m1a1+m2a2m1+m2Herem1,m2=Mass  of…

Q: The centre of mass of a non-uniform rod of length 4 m whose mass per unit length is K = 3x kg/m,…

A: Given: length=4m. mass per unit length: k=3x kg/m. To find: the distance of center of mass from the…

Q: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube,…

A: For a given mass distribution, its center of mass is a unique position where the entire mass of the…

Q: a shape is on an x-y axis, beginning at x = 0.  The bottom of the shape is 25 cm long and it reaches…

A:

Q: The measure of the linear density at a point of a rod varies directly as the third power of the…

A:

Q: The mass of Earth is 5.972×1024 kg and its orbital radius is an average of 1.496×1011 m. Calculate…

A:

Q: The measure of the linear density at a point on a rod varies directly as the fourth power of the…

A: Length of the rod L=2 m Mass of the rod m=64/5 kg Linear density is the mass per length from…

Q: Find the moments Mx and My and the center of mass of the system of masses. m1 = 6, m2 = 7, m3 = 1…

A:

Q: A uniform meter stick has a mass m1 = 10.0 kg placed at 100.0 cm mark and another mass m2 = 20.0 kg…

A: Given that, First mass m1=10.0 kg Distance of m1= 100.0 cm Another mass m2=20.0 kg Distance of m2 =…

Q: The mass of Earth is 5.972×1024 kg and its orbital radius is an average of 1.496×1011 m . Calculate…

A: Mass of earth, m = 5.972 x 1024 kg  radius, r = 1.496 x 1011 m

Q: A bullet of mass 3.6 g strikes a ballistic pendulum of mass 1.0 kg. The center of mass of the…

A:

Q: Find the center of mass coordinates XCM y YCM of the arrangement of masses shown. Assume that the…

A:

Q: What is the linear momentum of a 600 kg object moving 25m/s?

A: Formula -  P= m×vWhere, P = Linear momentum m = Mass  v = Velocity Given values -  m =600 kg v = 25…

Q: A lamina occupies the region inside the circle x^2+y^2=16 but outside the circle x^2+y^2=64 The…

A: Given:The density at each point is inversely proportional to its distance:

Q: Two identical masses, m are separated by a distance, d. If the masses weigh 5kg and separated by…

A: Given : Two identical masses, each of mass, m = 5kg Distance between two masses, d=2.5 m   To…

Q: We watch two identical astronomical bodies A and B, each of mass m, fall toward each other from rest…

A: Since there are multiple sub parts posted, we will answer the first three sub parts. a) The…

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).