Hooke’s Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as: F = -kx where F is the restoring force exerted by the spring k is the spring constant andRead more
Hooke’s Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as:
F = -kx
where F is the restoring force exerted by the spring k is the spring constant and x is the displacement from the equilibrium position.
Experimental Verification:
To verify Hooke’s Law experimentally, the following steps can be followed:
1. Setup: Attach a spring vertically to a fixed support and hang weights from the free end of the spring. Use a ruler or measuring tape to measure the displacement.
2. Apply Weights: Gradually add known weights to the spring and measure the extension (displacement) of the spring each time a weight is added. Ensure that the weights are added incrementally and the spring is not overstretched.
3. Record Data: Record the weight applied (force) and the corresponding displacement of the spring.
4. Plotting Graph: Plot a graph of the applied force (y-axis) against the displacement (x-axis). According to Hooke’s Law, the graph should be a straight line passing through the origin, indicating that the force is directly proportional to the displacement.
5. Determine the Spring Constant: The slope of the linear graph gives the value of the spring constant (k), confirming the validity of Hooke’s Law.
By conducting this experiment, one can observe that the extension of the spring is proportional to the applied force, thereby verifying Hooke’s Law.
When a disc rolls down an inclined plane, it has two types of kinetic energy: translational and rotational. The translational kinetic energy is due to the movement of the center of mass of the disc along the incline, while the rotational kinetic energy is due to the disc spinning around its axis asRead more
When a disc rolls down an inclined plane, it has two types of kinetic energy: translational and rotational. The translational kinetic energy is due to the movement of the center of mass of the disc along the incline, while the rotational kinetic energy is due to the disc spinning around its axis as it rolls.
For the solid disc, its moment of inertia plays an important role in determining how the energy is distributed between these two types of kinetic energy. For the disc that rolls without slipping, there exists a relationship between its linear velocity and its angular velocity, connecting the translational motion with the rotational motion.
When the total kinetic energy of the disc is analyzed, it is evident that the rotational kinetic energy is a part of the total energy. Once the contributions of both translational and rotational kinetic energy are evaluated, it is found that the ratio of the rotational kinetic energy to the total kinetic energy of a rolling disc is one to three. This means that for every part of kinetic energy contributed by rotation, three parts are from translation, thereby showing the balance between these two forms of energy in rolling motion.
When a body is projected from the ground at an angle to the horizontal, its angular momentum about the position of projection changes as it moves through its entire flight. At first, the body has angular momentum, depending on its speed and the distance between the point of projection and its centerRead more
When a body is projected from the ground at an angle to the horizontal, its angular momentum about the position of projection changes as it moves through its entire flight. At first, the body has angular momentum, depending on its speed and the distance between the point of projection and its center of mass, respectively. However, as the body continues through its trajectory, gravitational forces are applied. The weight of the body creates a torque about the point of projection, which affects its angular momentum.
As the body rises, the vertical component of its velocity decreases due to gravity, and it eventually reaches its maximum height before descending. During this time, the torque exerted by gravity continuously alters the angular momentum. Since the gravitational force always acts vertically downward through the centre of mass, the distance between line of action of gravitational force and pivot changes due to motion. Therefore, a loss of angular momentum occurs due to rotation at the original axis. All the angular momentum is reduced during this whole course of motion in the projected body due to both gravitational torque as well as displacement of the moving body with the pivot point.
Angular momentum is a concept in physics classed as a vector quantity because of its dual nature of having magnitude as well as direction; it is associated with the rotation of an object and can be thought of as the amount of motion that a body possesses while rotating about an axis. In contrast, woRead more
Angular momentum is a concept in physics classed as a vector quantity because of its dual nature of having magnitude as well as direction; it is associated with the rotation of an object and can be thought of as the amount of motion that a body possesses while rotating about an axis. In contrast, work and potential energy are scalar quantities, which have only magnitude and no direction; they can give no information about the rotational properties of a system.
To illustrate further, work is the transfer of energy when a force is applied over a distance, whereas potential energy describes the stored energy of an object based on the position in a gravitational field. Similarly, electric current is also a scalar quantity quantifying the flow of electric charge in a circuit.
Angular momentum plays a very crucial role in many physical scenarios that explain the dynamics of rotating bodies, such as planets, spinning tops, and wheels. In an isolated system, it remains conserved, which means that the total angular momentum will not change unless acted upon by an external torque. The conservation principle is important for predicting the behavior of rotating systems both in classical and modern physics.
The moment of inertia about the axis of rotation is merely a function of the distribution of its mass with regards to that axis; for a given mass and radius for a ring, it represents how the same mass is concentrated at the distance uniformly distributed from its center. However, if we were to consiRead more
The moment of inertia about the axis of rotation is merely a function of the distribution of its mass with regards to that axis; for a given mass and radius for a ring, it represents how the same mass is concentrated at the distance uniformly distributed from its center. However, if we were to consider it about one of its diameters, things would change based upon the principles of rotational dynamics.
By the perpendicular axes theorem, for any planar object, the moment of inertia about an axis perpendicular to its plane equals the sum of its moments of inertia about two mutually perpendicular axes lying in the plane and passing through the same point. In the case of a ring, the two perpendicular axes in its plane are its diameters, and they are identical due to symmetry. Therefore, the moment of inertia about a single diameter is half of that about the perpendicular axis through its center.
This relation further shows that moment of inertia is dependent on the geometry as well as the orientation of the axis of rotation. For the ring, the moment of inertia about its diameter comes out to be half the moment of inertia.
State Hooke’s law. How can it be verified experimentally?
Hooke’s Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as: F = -kx where F is the restoring force exerted by the spring k is the spring constant andRead more
Hooke’s Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as:
F = -kx
where F is the restoring force exerted by the spring k is the spring constant and x is the displacement from the equilibrium position.
Experimental Verification:
To verify Hooke’s Law experimentally, the following steps can be followed:
1. Setup: Attach a spring vertically to a fixed support and hang weights from the free end of the spring. Use a ruler or measuring tape to measure the displacement.
2. Apply Weights: Gradually add known weights to the spring and measure the extension (displacement) of the spring each time a weight is added. Ensure that the weights are added incrementally and the spring is not overstretched.
3. Record Data: Record the weight applied (force) and the corresponding displacement of the spring.
4. Plotting Graph: Plot a graph of the applied force (y-axis) against the displacement (x-axis). According to Hooke’s Law, the graph should be a straight line passing through the origin, indicating that the force is directly proportional to the displacement.
5. Determine the Spring Constant: The slope of the linear graph gives the value of the spring constant (k), confirming the validity of Hooke’s Law.
By conducting this experiment, one can observe that the extension of the spring is proportional to the applied force, thereby verifying Hooke’s Law.
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A disc is rolling on the inclined plane. What is the ratio of its rotation KE to the total KE?
When a disc rolls down an inclined plane, it has two types of kinetic energy: translational and rotational. The translational kinetic energy is due to the movement of the center of mass of the disc along the incline, while the rotational kinetic energy is due to the disc spinning around its axis asRead more
When a disc rolls down an inclined plane, it has two types of kinetic energy: translational and rotational. The translational kinetic energy is due to the movement of the center of mass of the disc along the incline, while the rotational kinetic energy is due to the disc spinning around its axis as it rolls.
For the solid disc, its moment of inertia plays an important role in determining how the energy is distributed between these two types of kinetic energy. For the disc that rolls without slipping, there exists a relationship between its linear velocity and its angular velocity, connecting the translational motion with the rotational motion.
When the total kinetic energy of the disc is analyzed, it is evident that the rotational kinetic energy is a part of the total energy. Once the contributions of both translational and rotational kinetic energy are evaluated, it is found that the ratio of the rotational kinetic energy to the total kinetic energy of a rolling disc is one to three. This means that for every part of kinetic energy contributed by rotation, three parts are from translation, thereby showing the balance between these two forms of energy in rolling motion.
Click here for more : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessA body is projected from the ground with some angle to the horizontal. What happens to the angular momentum about the initial position in this motion?
When a body is projected from the ground at an angle to the horizontal, its angular momentum about the position of projection changes as it moves through its entire flight. At first, the body has angular momentum, depending on its speed and the distance between the point of projection and its centerRead more
When a body is projected from the ground at an angle to the horizontal, its angular momentum about the position of projection changes as it moves through its entire flight. At first, the body has angular momentum, depending on its speed and the distance between the point of projection and its center of mass, respectively. However, as the body continues through its trajectory, gravitational forces are applied. The weight of the body creates a torque about the point of projection, which affects its angular momentum.
As the body rises, the vertical component of its velocity decreases due to gravity, and it eventually reaches its maximum height before descending. During this time, the torque exerted by gravity continuously alters the angular momentum. Since the gravitational force always acts vertically downward through the centre of mass, the distance between line of action of gravitational force and pivot changes due to motion. Therefore, a loss of angular momentum occurs due to rotation at the original axis. All the angular momentum is reduced during this whole course of motion in the projected body due to both gravitational torque as well as displacement of the moving body with the pivot point.
Click here for more : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessWhich is a vector quantity?
Angular momentum is a concept in physics classed as a vector quantity because of its dual nature of having magnitude as well as direction; it is associated with the rotation of an object and can be thought of as the amount of motion that a body possesses while rotating about an axis. In contrast, woRead more
Angular momentum is a concept in physics classed as a vector quantity because of its dual nature of having magnitude as well as direction; it is associated with the rotation of an object and can be thought of as the amount of motion that a body possesses while rotating about an axis. In contrast, work and potential energy are scalar quantities, which have only magnitude and no direction; they can give no information about the rotational properties of a system.
To illustrate further, work is the transfer of energy when a force is applied over a distance, whereas potential energy describes the stored energy of an object based on the position in a gravitational field. Similarly, electric current is also a scalar quantity quantifying the flow of electric charge in a circuit.
Angular momentum plays a very crucial role in many physical scenarios that explain the dynamics of rotating bodies, such as planets, spinning tops, and wheels. In an isolated system, it remains conserved, which means that the total angular momentum will not change unless acted upon by an external torque. The conservation principle is important for predicting the behavior of rotating systems both in classical and modern physics.
Click here for more: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessMoment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is l. What is the moment of inertia about its diameter?
The moment of inertia about the axis of rotation is merely a function of the distribution of its mass with regards to that axis; for a given mass and radius for a ring, it represents how the same mass is concentrated at the distance uniformly distributed from its center. However, if we were to consiRead more
The moment of inertia about the axis of rotation is merely a function of the distribution of its mass with regards to that axis; for a given mass and radius for a ring, it represents how the same mass is concentrated at the distance uniformly distributed from its center. However, if we were to consider it about one of its diameters, things would change based upon the principles of rotational dynamics.
By the perpendicular axes theorem, for any planar object, the moment of inertia about an axis perpendicular to its plane equals the sum of its moments of inertia about two mutually perpendicular axes lying in the plane and passing through the same point. In the case of a ring, the two perpendicular axes in its plane are its diameters, and they are identical due to symmetry. Therefore, the moment of inertia about a single diameter is half of that about the perpendicular axis through its center.
This relation further shows that moment of inertia is dependent on the geometry as well as the orientation of the axis of rotation. For the ring, the moment of inertia about its diameter comes out to be half the moment of inertia.
Click here for more: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See less