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Analogue of mass in rotational motion is
The analogue of mass in rotational motion is called moment of inertia. Like mass, moment of inertia determines the resistance of an object to changes in its motion: now to rotational motion instead of linear motion. The property depends not only on the mass of the object but also on how that mass isRead more
The analogue of mass in rotational motion is called moment of inertia. Like mass, moment of inertia determines the resistance of an object to changes in its motion: now to rotational motion instead of linear motion. The property depends not only on the mass of the object but also on how that mass is distributed relative to the axis of rotation.
For example, take the ring and sphere both of identical mass and radius, but let one be an ordinary ring that can be placed outside the edge where the most amount of the mass is localized in comparison with a solid sphere whose mass remains concentrated closer to the axis, resulting in higher moment of inertia of the former over the latter, meaning one will require higher torque to cause angular acceleration if its angular velocity was the same for both.
The moment of inertia is very important in rotational dynamics. It is the rotational counterpart of mass in linear motion. Other quantities such as angular momentum and radius of gyration are related to rotational motion but do not directly represent mass. Angular momentum is like linear momentum in rotation, and the radius of gyration provides a measure of mass distribution. Thus, the moment of inertia is the true rotational equivalent of mass.
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See lessIf a person standing on a rotating disc stretches out his hands, the angular speed will
When a person standing on a rotating disc stretches out his hands, his angular speed decreases. This is because of the law of conservation of angular momentum, where the angular momentum of a system remains the same if no external torque acts on it. Angular momentum is the product of the moment of iRead more
When a person standing on a rotating disc stretches out his hands, his angular speed decreases. This is because of the law of conservation of angular momentum, where the angular momentum of a system remains the same if no external torque acts on it.
Angular momentum is the product of the moment of inertia and angular velocity. If he stretches his arms out to his sides, the person increases his moment of inertia, as the mass distribution moves farther from the axis of rotation. In order to conserve angular momentum, the angular velocity-or angular speed-must decrease correspondingly.
This principle is often seen in figure skating or gymnastics. A spinning skater can raise his speed by retracting his arms so that he reduces his moment of inertia and increases his angular velocity. He slows down if he stretches out his arms.
This principle also applies to many real-world circumstances, such as athletes using body movements to control rotational speed or space probes adjusting the orientation of their trajectory in space. In such a case, by extending their arms, the moment of inertia is increased, leading to a decrease in angular velocity to keep angular momentum constant.
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See lessA sphere of radius r is rolling without sliding. What is ratio of rotational kinetic energy and total kinetic energy associated with the sphere?
Total kinetic energy, in this case of a rolling sphere, consists of two parts: rotational kinetic energy and translational kinetic energy. Rotational kinetic energy is that caused by rotation of the sphere around its axis of rotation while the translational kinetic energy arises due to linear motionRead more
Total kinetic energy, in this case of a rolling sphere, consists of two parts: rotational kinetic energy and translational kinetic energy. Rotational kinetic energy is that caused by rotation of the sphere around its axis of rotation while the translational kinetic energy arises due to linear motion of the sphere. In rolling motion, these two forms of energy are coupled through the condition that the sphere rolls without sliding, implying there is no relative motion at the point of contact with the surface.
Rotational kinetic energy for a solid sphere is a particular fraction of total kinetic energy. For the given problem, the rotational kinetic energy: total kinetic energy ratio was 2/7. This suggests that the rotational part contributes less to the total energy as compared to the translational part. The remaining 5/7 is all taken up by the translation kinetic energy.
This concept is important in understanding how energy is distributed in rolling systems. It has practical applications in fields like mechanics, engineering, and physics education, helping to analyze the motion of rolling objects such as balls, wheels, and gears. The ratio emphasizes the importance of both rotational and translational dynamics in rolling motion.
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See lessMoment of inertia of an object does not depend upon
The moment of inertia is a property that tells us how a rotating object resists the change in angular acceleration. The theoretical background assumes mass, the distribution of this mass relative to the axis, and the selected axis itself for the three parameters. The mass and how far away from the aRead more
The moment of inertia is a property that tells us how a rotating object resists the change in angular acceleration. The theoretical background assumes mass, the distribution of this mass relative to the axis, and the selected axis itself for the three parameters. The mass and how far away from the axis it lies give an object a higher moment of inertia. For instance, a hollow ring has a greater moment of inertia than an equivalent solid disc of the same mass and radius because its mass is distributed further from the axis. However, the moment of inertia is independent of the angular velocity of the object. Angular velocity explains how fast an object is spinning, but this does not contribute to the intrinsic resistance to its rotation. It means that irrespective of whether it is spinning rapidly or slowly, the moment of inertia remains unchanged because it only depends on its physical structure and the axis about which it rotates.
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See lessThe horizontal range of a projectile is maximum when the angle of projection is:
The horizontal range of a projectile is given by R = u² Sin 2θ/g. The range is maximum when sin2θ = 1, which occurs at θ = 45°. This question related to Chapter 3 physics Class 11th NCERT. From the Chapter 3. Motion in Plane. Give answer according to your understanding. For more please visit here: hRead more
The horizontal range of a projectile is given by R = u² Sin 2θ/g. The range is maximum when sin2θ = 1, which occurs at θ = 45°. This question related to Chapter 3 physics Class 11th NCERT. From the Chapter 3. Motion in Plane. Give answer according to your understanding.
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