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Questions and Answers
What is the physical significance of the equation MA = F1 + F2 + ... + Fn?
What is the physical significance of the equation MA = F1 + F2 + ... + Fn?
- It states that the acceleration of the centre of mass of a system is equal to the vector sum of accelerations of individual particles.
- It represents the conservation of momentum of a closed system.
- 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. (correct)
- It is a mathematical manipulation of the equation of motion of individual particles.
What is the assumption made while differentiating the equation for the centre of mass with respect to time?
What is the assumption made while differentiating the equation for the centre of mass with respect to time?
- The masses of the particles change with time.
- The particles are at rest.
- The particles are moving with constant velocity.
- The masses of the particles are constant. (correct)
What is the meaning of F1, F2, ..., Fn in the equation MA = F1 + F2 + ... + Fn?
What is the meaning of F1, F2, ..., Fn in the equation MA = F1 + F2 + ... + Fn?
- The forces exerted by the first, second, ..., nth particle on the rest of the system.
- The net forces acting on the first, second, ..., nth particle. (correct)
- The forces exerted by the rest of the system on the first, second, ..., nth particle.
- The internal forces between the particles.
Why do we consider the centre of mass in the study of motion of a system of particles?
Why do we consider the centre of mass in the study of motion of a system of particles?
What is the significance of the equation MR = m1r1 + m2r2 + ... + mn rn?
What is the significance of the equation MR = m1r1 + m2r2 + ... + mn rn?
What is the primary condition for the applicability of Equation 6.11?
What is the primary condition for the applicability of Equation 6.11?
What is the main advantage of treating extended bodies as systems of particles?
What is the main advantage of treating extended bodies as systems of particles?
What is an assumption that is no longer required when applying Equation 6.11?
What is an assumption that is no longer required when applying Equation 6.11?
What is the significance of the sum of internal forces in Equation 6.10?
What is the significance of the sum of internal forces in Equation 6.10?
What is the fundamental concept that Equation 6.11 is based on?
What is the fundamental concept that Equation 6.11 is based on?
Study Notes
Motion of Centre of Mass
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Description
Understanding the physical importance of centre of mass for a system of particles, including equations for momentum and velocity.
