10 Questions
What is the physical significance of the equation MA = F1 + F2 + ... + Fn?
It shows that the total mass of a system of particles times the acceleration of its centre of mass is the vector sum of all the forces acting on the system.
What is the assumption made while differentiating the equation for the centre of mass with respect to time?
The masses of the particles are constant.
What is the meaning of F1, F2, ..., Fn in the equation MA = F1 + F2 + ... + Fn?
The net forces acting on the first, second, ..., nth particle.
Why do we consider the centre of mass in the study of motion of a system of particles?
To represent the overall motion of the system as a whole.
What is the significance of the equation MR = m1r1 + m2r2 + ... + mn rn?
It defines the centre of mass of a system of particles.
What is the primary condition for the applicability of Equation 6.11?
The internal forces within the system should be zero.
What is the main advantage of treating extended bodies as systems of particles?
It simplifies the analysis of translational motion.
What is an assumption that is no longer required when applying Equation 6.11?
The rotational motion and/or internal motion of the particles were either absent or negligible.
What is the significance of the sum of internal forces in Equation 6.10?
It is zero and therefore does not affect the equation.
What is the fundamental concept that Equation 6.11 is based on?
Newton's third law of motion.
Study Notes
Motion of Centre of Mass
-
The centre of mass of a system of particles moves according to the equation: MA = F_ext, where M is the total mass of the system, A is the acceleration of the centre of mass, and F_ext is the sum of all external forces acting on the particles.
-
This equation states that the centre of mass of a system of particles moves as if all the mass of the system was concentrated at the centre of mass and all the external forces were applied at that point.
-
To determine the motion of the centre of mass, no knowledge of internal forces of the system of particles is required; only the external forces need to be known.
-
The equation MA = F_ext is applicable to any system of particles, regardless of the nature of the system or the motion of its individual particles.
-
The centre of mass moves according to the equation MA = F_ext, whether the system is a collection of particles with internal motions, or a rigid body with translational and/or rotational motion.
-
In earlier studies, extended bodies were treated as single particles, but now we can treat them as systems of particles and obtain the translational component of their motion by assuming the mass of the whole system is concentrated at the centre of mass and all external forces act at the centre of mass.
-
The centre of mass moves according to the equation MA = F_ext, which implies that the total mass of a system of particles times the acceleration of its centre of mass is the vector sum of all the forces acting on the system of particles.
Understanding the physical importance of centre of mass for a system of particles, including equations for momentum and velocity.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
