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State the dimensional formula of work.
Dimensions of work = [𝑀^1𝐿^2𝑇^−2]. For more please visit here: https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-1/
Dimensions of work = [𝑀^1𝐿^2𝑇^−2].
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-1/
Obtain an expression for the work done by a torque. Hence write the expression for power.
The work done by a torque in rotating an object depends on the torque applied and the angular displacement through which the object rotates. If a torque is applied to a body, that body would rotate about an axis. The amount of work done is directly proportional to both the magnitude of the torque anRead more
The work done by a torque in rotating an object depends on the torque applied and the angular displacement through which the object rotates. If a torque is applied to a body, that body would rotate about an axis. The amount of work done is directly proportional to both the magnitude of the torque and the angle through which the object moves. In essence, if a greater torque is applied or if the object rotates through a larger angle, more work is done.
Power, on the other hand, measures the rate at which this work is done. It is defined as the rate at which work is being done over time. For the case of rotational motion, power is related to the work done by the torque and also the time taken to that work. To be more specific, power will be calculated in terms of how much work is done within a certain given time frame when an object is rotated.
This implies that the power developed in a rotating system is dependent on the torque applied to the object as well as its speed of rotation. Understanding torque, work, and power interdependence is thus very important for the analysis of rotational systems and their efficiency in doing work.
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See lessWrite an expression for torque in three-dimensional motion. Hence write the expressions for the rectangular components of torque.
Torque in three-dimensional motion refers to the rotational force which is brought about by applying a force at some distance from an axis of rotation. In this sense, torque may be interpreted as the result of a force applied to cause rotation about an axis. To describe torque in three dimensions weRead more
Torque in three-dimensional motion refers to the rotational force which is brought about by applying a force at some distance from an axis of rotation. In this sense, torque may be interpreted as the result of a force applied to cause rotation about an axis. To describe torque in three dimensions we consider the position vector that extends from the axis of rotation to where the force is applied as well as the force vector. The torque, here, can then be represented by its rectangular components along the three axes.
The torque component in the x-direction is given by the product of the y-coordinate of the position vector and the z-component of the force minus the product of the z-coordinate of the position vector and the y-component of the force. The y-component of the torque is the z-coordinate of the position vector multiplied by the x-component of the force, minus the product of the x-coordinate of the position vector and the z-component of the force. Lastly, the z-component of torque comes from the x and y components of the position and force vectors. This approach allows for a detailed analysis of rotational motion in three dimensions.
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See lessExplain the use of dimensional equations in unit conversion.
They ensure that derived units correctly match the base units during calculations. This question related to Chapter 1 physics Class 11th NCERT. From the Chapter 1. Units and Measurements. Give answer according to your understanding. For more please visit here: https://www.tiwariacademy.com/ncert-solRead more
They ensure that derived units correctly match the base units during calculations. This question related to Chapter 1 physics Class 11th NCERT. From the Chapter 1. Units and Measurements. Give answer according to your understanding.
For more please visit here:
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Show that the magnitude of torque = magnitude of force x moment arm. Also show that only the angular component of the force is responsible for producing torque.
The magnitude of torque is defined as the product of the magnitude of the force applied and the moment arm, which is the perpendicular distance from the axis of rotation to the line of action of the force. This relationship highlights that the effectiveness of a force in generating rotation dependsRead more
The magnitude of torque is defined as the product of the magnitude of the force applied and the moment arm, which is the perpendicular distance from the axis of rotation to the line of action of the force. This relationship highlights that the effectiveness of a force in generating rotation depends on both the size of the applied force and its distance from the axis. If the force is applied directly at the pivot, then the moment arm is zero, and torque is not produced. However, in the case of application of force with an angle to the pivot, the moment arm can be a maximum, giving a greater torque effect.
Furthermore, only the angular component of the force results in the torque. This is because torque is produced by the force that acts perpendicular to the radius vector, which results in rotation. If a force is applied at an angle to the radius vector, only the component perpendicular contributes to the torque. The component of the force that acts parallel to the radius does not produce rotational motion because it merely pulls or pushes toward the axis without causing rotation. Therefore, understanding the magnitude of the force and the angle at which it is applied is critical in analyzing rotational motion.
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