Angular momentum, being a vector, describes the rotational motion of a body. The expression for angular momentum can be given through the vector product between the position vector and the linear momentum vector. It therefore characterizes an object's position relative to a specified point of rotatiRead more
Angular momentum, being a vector, describes the rotational motion of a body. The expression for angular momentum can be given through the vector product between the position vector and the linear momentum vector. It therefore characterizes an object’s position relative to a specified point of rotation while the linear momentum vector further characterizes the motion of the object based on its mass and velocity.
When these two vectors are cross multiplied, the resulting angular momentum vector encapsulates the magnitude and direction of the rotational motion. The magnitude of the angular momentum will reflect the distance of the object from the axis of rotation and its velocity. This way, it will illustrate how these factors contribute to the rotational effect of the object.
The direction of the angular momentum vector is found using the right-hand rule. This rule is to be applied in the following: One points fingers of their right hand in the direction of the position vector. Then curls their fingers toward the direction of the linear momentum vector. The thumb will then point in the direction of the angular momentum vector. This directional aspect is important because it gives the axis of rotation and the sense of the angular motion, so one can get a complete understanding of the dynamics of rotating systems.
Angular momentum is the rotational motion of a particle about a reference point. To express it in terms of rectangular components, we look at the position and linear momentum vectors of the particle. The position vector describes the location of the particle relative to the reference point, while thRead more
Angular momentum is the rotational motion of a particle about a reference point. To express it in terms of rectangular components, we look at the position and linear momentum vectors of the particle. The position vector describes the location of the particle relative to the reference point, while the linear momentum vector describes the motion of the particle based on its mass and velocity. These vectors are decomposed into components along the x, y, and z axes.
Angular momentum is defined as the cross product of the position vector and the linear momentum vector. The resulting angular momentum vector has three components, one for each of the three spatial axes. These components depend on the perpendicular contributions of the position and momentum vectors along the other two axes.
For example, the angular momentum in the x-direction is generated by the components perpendicular to it along the y and z directions. In a similar fashion, the angular momentum in the y-direction comes from the contributions along the z and x directions, and so forth for the z-direction.
This method allows the rotational behavior of a particle to be analyzed in three-dimensional space, showing how different components of position and momentum contribute to the overall angular momentum.
Angular momentum is a very important concept in physics that describes the rotational motion of an object about a specific axis. It can be expressed in terms of the rectangular components of linear momentum and position vectors in three-dimensional space. To help understand this relationship, take aRead more
Angular momentum is a very important concept in physics that describes the rotational motion of an object about a specific axis. It can be expressed in terms of the rectangular components of linear momentum and position vectors in three-dimensional space.
To help understand this relationship, take an object with the characteristics of position in space, which is represented with a position vector, and the motion represented with a linear momentum vector. The position vector gives the location of the object with respect to a reference point. A linear momentum vector gives the amount of motion that the object has, based on its mass and velocity.
Angular momentum is computed as the cross product of the position vector and the linear momentum vector. The result is an angular momentum vector that reflects the magnitude and direction of the rotational motion of the object. The components of this angular momentum vector can be obtained from the corresponding components of the position and momentum vectors.
In essence, the angular momentum vector brings to light how motion depends on position relative to an axis of rotation. Such a representation is useful for many analyses that are required in rotating systems in various domains, including mechanics, astrophysics, and engineering, which necessarily must consider the rotational behavior of objects.
Without gravitational force, the central force of gravity would not affect a satellite so that it will no longer orbit about the Earth. Gravitational force is what provides the inflected force required for a satellite orbiting to trace a curvilinear path. If that force will be removed, a satellite caRead more
Without gravitational force, the central force of gravity would not affect a satellite so that it will no longer orbit about the Earth. Gravitational force is what provides the inflected force required for a satellite orbiting to trace a curvilinear path. If that force will be removed, a satellite cannot have the tendency to orbit around the earth anymore as there is an inward force to hold and maintain it on a curvilinear trajectory, like a circular or elliptical orbit.
According to Newton’s first law of motion, an object in motion will continue moving in a straight line with constant velocity unless acted upon by an external force. So if the gravitational force were to suddenly disappear, the satellite would stop its curved motion and move tangentially to its original orbit at the same velocity \(v\) it had at the moment gravity vanished.
This tangent motion results because the speed of a satellite at any location on an orbit always points along the tangent of the curve in its trajectory. Without gravitational force, the satellite would just go along this tangent forever. The motion, being rectilinear, could not pull the satellite toward its orbital path or back to Earth, since it would be lacking in a centripetal force. It would drift through space, and Earth’s influence would be felt no longer.
Escape velocity is the minimum speed a particle or object must have to overcome the gravitational pull of a planet or celestial body and leave space without any further propulsion. This velocity depends on the mass and radius of the celestial body (like Earth) and the gravitational constant, but notRead more
Escape velocity is the minimum speed a particle or object must have to overcome the gravitational pull of a planet or celestial body and leave space without any further propulsion. This velocity depends on the mass and radius of the celestial body (like Earth) and the gravitational constant, but not on the mass of the escaping particle itself.
This is because the gravitational force exerted on the particle and the kinetic energy needed to escape are proportional to the mass of the particle. In the case of calculating escape velocity, the mass of the particle cancels out, and a value that depends solely on the properties of the celestial body remains.
For instance, the escape velocity on earth is approximately 11.2 km/s just above the surface, a value applicable to any body, no matter how slight its mass may be—like a stone, a satellite, or a spacecraft. As such, the mass of the escaping particle does not affect the escape velocity in any way; it would be universal for a celestial body.
Explain how angular momentum can be expressed as the vector product of two vectors. How is its direction determined?
Angular momentum, being a vector, describes the rotational motion of a body. The expression for angular momentum can be given through the vector product between the position vector and the linear momentum vector. It therefore characterizes an object's position relative to a specified point of rotatiRead more
Angular momentum, being a vector, describes the rotational motion of a body. The expression for angular momentum can be given through the vector product between the position vector and the linear momentum vector. It therefore characterizes an object’s position relative to a specified point of rotation while the linear momentum vector further characterizes the motion of the object based on its mass and velocity.
When these two vectors are cross multiplied, the resulting angular momentum vector encapsulates the magnitude and direction of the rotational motion. The magnitude of the angular momentum will reflect the distance of the object from the axis of rotation and its velocity. This way, it will illustrate how these factors contribute to the rotational effect of the object.
The direction of the angular momentum vector is found using the right-hand rule. This rule is to be applied in the following: One points fingers of their right hand in the direction of the position vector. Then curls their fingers toward the direction of the linear momentum vector. The thumb will then point in the direction of the angular momentum vector. This directional aspect is important because it gives the axis of rotation and the sense of the angular motion, so one can get a complete understanding of the dynamics of rotating systems.
for more info: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessExpress angular momentum in terms of the rectangular components of linear momentum and position vectors.
Angular momentum is the rotational motion of a particle about a reference point. To express it in terms of rectangular components, we look at the position and linear momentum vectors of the particle. The position vector describes the location of the particle relative to the reference point, while thRead more
Angular momentum is the rotational motion of a particle about a reference point. To express it in terms of rectangular components, we look at the position and linear momentum vectors of the particle. The position vector describes the location of the particle relative to the reference point, while the linear momentum vector describes the motion of the particle based on its mass and velocity. These vectors are decomposed into components along the x, y, and z axes.
Angular momentum is defined as the cross product of the position vector and the linear momentum vector. The resulting angular momentum vector has three components, one for each of the three spatial axes. These components depend on the perpendicular contributions of the position and momentum vectors along the other two axes.
For example, the angular momentum in the x-direction is generated by the components perpendicular to it along the y and z directions. In a similar fashion, the angular momentum in the y-direction comes from the contributions along the z and x directions, and so forth for the z-direction.
This method allows the rotational behavior of a particle to be analyzed in three-dimensional space, showing how different components of position and momentum contribute to the overall angular momentum.
Click here for more:- https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessExpress angular momentum in terms of the rectangular components of linear momentum and position vectors.
Angular momentum is a very important concept in physics that describes the rotational motion of an object about a specific axis. It can be expressed in terms of the rectangular components of linear momentum and position vectors in three-dimensional space. To help understand this relationship, take aRead more
Angular momentum is a very important concept in physics that describes the rotational motion of an object about a specific axis. It can be expressed in terms of the rectangular components of linear momentum and position vectors in three-dimensional space.
To help understand this relationship, take an object with the characteristics of position in space, which is represented with a position vector, and the motion represented with a linear momentum vector. The position vector gives the location of the object with respect to a reference point. A linear momentum vector gives the amount of motion that the object has, based on its mass and velocity.
Angular momentum is computed as the cross product of the position vector and the linear momentum vector. The result is an angular momentum vector that reflects the magnitude and direction of the rotational motion of the object. The components of this angular momentum vector can be obtained from the corresponding components of the position and momentum vectors.
In essence, the angular momentum vector brings to light how motion depends on position relative to an axis of rotation. Such a representation is useful for many analyses that are required in rotating systems in various domains, including mechanics, astrophysics, and engineering, which necessarily must consider the rotational behavior of objects.
Check this for more : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessA Satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will
Without gravitational force, the central force of gravity would not affect a satellite so that it will no longer orbit about the Earth. Gravitational force is what provides the inflected force required for a satellite orbiting to trace a curvilinear path. If that force will be removed, a satellite caRead more
Without gravitational force, the central force of gravity would not affect a satellite so that it will no longer orbit about the Earth. Gravitational force is what provides the inflected force required for a satellite orbiting to trace a curvilinear path. If that force will be removed, a satellite cannot have the tendency to orbit around the earth anymore as there is an inward force to hold and maintain it on a curvilinear trajectory, like a circular or elliptical orbit.
According to Newton’s first law of motion, an object in motion will continue moving in a straight line with constant velocity unless acted upon by an external force. So if the gravitational force were to suddenly disappear, the satellite would stop its curved motion and move tangentially to its original orbit at the same velocity \(v\) it had at the moment gravity vanished.
This tangent motion results because the speed of a satellite at any location on an orbit always points along the tangent of the curve in its trajectory. Without gravitational force, the satellite would just go along this tangent forever. The motion, being rectilinear, could not pull the satellite toward its orbital path or back to Earth, since it would be lacking in a centripetal force. It would drift through space, and Earth’s influence would be felt no longer.
See lessIn what manner, does the escape velocity of a particle depend upon its mass?
Escape velocity is the minimum speed a particle or object must have to overcome the gravitational pull of a planet or celestial body and leave space without any further propulsion. This velocity depends on the mass and radius of the celestial body (like Earth) and the gravitational constant, but notRead more
Escape velocity is the minimum speed a particle or object must have to overcome the gravitational pull of a planet or celestial body and leave space without any further propulsion. This velocity depends on the mass and radius of the celestial body (like Earth) and the gravitational constant, but not on the mass of the escaping particle itself.
This is because the gravitational force exerted on the particle and the kinetic energy needed to escape are proportional to the mass of the particle. In the case of calculating escape velocity, the mass of the particle cancels out, and a value that depends solely on the properties of the celestial body remains.
For instance, the escape velocity on earth is approximately 11.2 km/s just above the surface, a value applicable to any body, no matter how slight its mass may be—like a stone, a satellite, or a spacecraft. As such, the mass of the escaping particle does not affect the escape velocity in any way; it would be universal for a celestial body.
See less