The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one's location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the coRead more
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one’s location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the core, at elevated heights, because the distance from the earth’s center now increases, gravitation diminishes. In both scenarios, the acceleration due to gravity is reduced since it is proportional to the mass and distance of the body involved. Such differences are essential for determining gravitational changes across different regions on Earth or within the surrounding space.
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses servinRead more
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses serving as weights. The position of the center of mass lies closer to the particle with the larger mass. If the masses are equal, the centre of mass is exactly between the two particles. The above concept applies universally to any two-particle system, regardless of the values of distances or mass.
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is aRead more
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is a weighted average of the individual particle velocities.
According to Newton’s second law, the change in momentum of the system is equal to the net external force. In the absence of external forces, the total momentum remains constant, implying that the velocity of the center of mass also remains constant.
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to theRead more
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to the heavier region. The shape of the body is also involved in this; symmetrical shapes have their center of mass at the center of symmetry, while asymmetrical shapes have it offset from that point. Disturbance in density would further shift the positions of the center of mass toward denser regions. For systems of bodies, further external forces or constraints can affect its position.
A particle is an idealized small-sized object with mass but negligible in size, and used in physics to simplify the problems by taking the objects as point masses. The system means a collection of particles or objects that are taken for analysis, and it may be isolated from the external influences oRead more
A particle is an idealized small-sized object with mass but negligible in size, and used in physics to simplify the problems by taking the objects as point masses. The system means a collection of particles or objects that are taken for analysis, and it may be isolated from the external influences or open to them. The forces exerted by the particles inside a system on each other do not affect the total momentum of the system, hence termed internal forces. In contrast, external forces act on the system from outside its boundaries, changing its momentum and influencing its overall motion. Understanding these concepts is essential for analyzing physical interactions and dynamics.
The acceleration due to gravity decreases with:
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one's location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the coRead more
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one’s location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the core, at elevated heights, because the distance from the earth’s center now increases, gravitation diminishes. In both scenarios, the acceleration due to gravity is reduced since it is proportional to the mass and distance of the body involved. Such differences are essential for determining gravitational changes across different regions on Earth or within the surrounding space.
See lessDerive an expression for the centre of mass of a two particle system from ab-inito.
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses servinRead more
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses serving as weights. The position of the center of mass lies closer to the particle with the larger mass. If the masses are equal, the centre of mass is exactly between the two particles. The above concept applies universally to any two-particle system, regardless of the values of distances or mass.
See lessShow that in the absence of any external force, the velocity of the centre of mass remains constant.
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is aRead more
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is a weighted average of the individual particle velocities.
See lessAccording to Newton’s second law, the change in momentum of the system is equal to the net external force. In the absence of external forces, the total momentum remains constant, implying that the velocity of the center of mass also remains constant.
State the factors on which the position of the centre of mass of a rigid body depends.
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to theRead more
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to the heavier region. The shape of the body is also involved in this; symmetrical shapes have their center of mass at the center of symmetry, while asymmetrical shapes have it offset from that point. Disturbance in density would further shift the positions of the center of mass toward denser regions. For systems of bodies, further external forces or constraints can affect its position.
See lessWhat is meant by a particle, a system and internal and external forces?
A particle is an idealized small-sized object with mass but negligible in size, and used in physics to simplify the problems by taking the objects as point masses. The system means a collection of particles or objects that are taken for analysis, and it may be isolated from the external influences oRead more
A particle is an idealized small-sized object with mass but negligible in size, and used in physics to simplify the problems by taking the objects as point masses. The system means a collection of particles or objects that are taken for analysis, and it may be isolated from the external influences or open to them. The forces exerted by the particles inside a system on each other do not affect the total momentum of the system, hence termed internal forces. In contrast, external forces act on the system from outside its boundaries, changing its momentum and influencing its overall motion. Understanding these concepts is essential for analyzing physical interactions and dynamics.
See less