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Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be
Let us determine the center of mass's speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.Read more
Let us determine the center of mass’s speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.
In the initial state, both particles are at rest and therefore have zero initial momentum. As they start moving toward one another, acceleration occurs due to the mutual gravitational attraction between the particles. The velocity of the center of mass is the main concept in this scenario, representing the overall motion of the system based on individual masses and their respective velocities.
Despite the fact that the particles are accelerating as they approach each other, the principle of conservation of momentum states that the center of mass is unchanged. The relative motion of the two particles will affect the center of mass, and since they are moving toward each other, the center of mass remains stationary. Thus, the effect of their combined motion is to produce no overall acceleration in the center of mass. Therefore, the speed of the center of mass of this system is zero, meaning that the motion of the individual particles does not alter the overall state of rest of the system.
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A diver in a swimming pool bends his head before diving. It
When a diver flexes his or her head and tucks the limbs before making a dive, he or she reduces his or her moment of inertia. Moment of inertia is defined as the mass distribution around an axis of rotation. Since the diver draws his or her mass closer to the axis of rotation, he or she reduces theRead more
When a diver flexes his or her head and tucks the limbs before making a dive, he or she reduces his or her moment of inertia. Moment of inertia is defined as the mass distribution around an axis of rotation. Since the diver draws his or her mass closer to the axis of rotation, he or she reduces the distribution. This is important in executing rotations properly during the dive.
This process involves the conservation of angular momentum. In the absence of an external torque on a system, the angular momentum is constant. By reducing the moment of inertia, the diver automatically increases their angular velocity, allowing for faster rotations. This technique is necessary to complete complex aerial maneuvers such as somersaults and twists within the short time available in the air.
Before diving, the diver tucks into an acock position so that rotation can take place rapidly, but at close proximity to the water edge, they extend their body, increasing the moment of inertia in order to bridle the speed of rotation, allowing for entry into the pool safely and precisely while minimizing splash and inflicting damage. This way, bending the head and body is essential for divers to achieve maximum rotational motion and execute complicated maneuvers with great accuracy.
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Joule second is the unit of
The unit is called the Joule second (J·s), and it's used to describe angular momentum-a concept in rotational motion. The rotational equivalent of linear momentum, angular momentum is a measure dependent on the body's rotational inertia and its angular velocity. Stated another way, it gives a measurRead more
The unit is called the Joule second (J·s), and it’s used to describe angular momentum-a concept in rotational motion. The rotational equivalent of linear momentum, angular momentum is a measure dependent on the body’s rotational inertia and its angular velocity. Stated another way, it gives a measure of how much motion an object possesses and how it’s distributed around the axis of rotation.
Angular momentum is applied to describe motion systems in the physical world, including spinning objects, rotating planets, and even quantum systems. In this case, the unit would be Joule second because it involves quantities like torque and time, which together reflect aspects of energy and motion in rotational contexts.
All the other quantities of the given choices are measured in totally different units. Linear momentum is measured in kilogram meter per second, work is measured in Joules, and pressure is measured in Pascal. The units also fit with the physical definitions and the mathematical formulation of the quantities concerned.
Accordingly, in the following set of choices, angular momentum would be measured in Joule seconds, presenting the uniqueness with respect to quantities for rotational motion study.
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An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver?
An automobile engine produces 100 kW power output while operating at a rotational speed of 1800 revolutions per minute. To find the torque it produces, we must understand the relationship between power and torque and the rotational speed. Power is the rate of working or transfer rate of energy whereRead more
An automobile engine produces 100 kW power output while operating at a rotational speed of 1800 revolutions per minute. To find the torque it produces, we must understand the relationship between power and torque and the rotational speed.
Power is the rate of working or transfer rate of energy whereas torque represents forces that would try to generate this rotational movement relative to a plane. Every turning motion causes distribution of torque but keeps producing work and then leads to maintain their angular velocities throughout.
First, the rotational speed is converted into a standard unit called radians per second, which is the common unit used in calculations involving rotational motion. Then, torque can be calculated by dividing power by angular velocity.
After all these, it is observed that the engine produces a torque of 531 Nm. This translates to the force the engine uses to rotate. It is expressed in newton-meters. Torque will be one of the most crucial factors in rating an engine, as it dictates acceleration and, consequently, doing work, for example, pushing heavy loads up steep inclines.
Hence, the torque developed by this engine is ideal for its applied power and speed.
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Which one is a vector quantity ?
Torque is a quantity that describes a force's capacity to produce or change rotation at an axis applied to an object. The size of the torque depends on both the applied force, the perpendicular distance from the axis to where the force has been applied called the lever arm, and on the angle made betRead more
Torque is a quantity that describes a force’s capacity to produce or change rotation at an axis applied to an object. The size of the torque depends on both the applied force, the perpendicular distance from the axis to where the force has been applied called the lever arm, and on the angle made between the two. The direction of the torque is determined using the right-hand rule: if the fingers of your right hand curl in the direction of the rotation caused by the force, then your thumb points in the direction of the torque vector.
Energy is a scalar quantity. Scalar quantities have magnitude but no direction. Energy cannot exist with their direction like length, area, and volume. It depends what type of energy it belongs to, like kinetic, potential, thermal, or electrical. No matter what kind of energy it is, it is a scalar quantity. Scalars are not vectors, but are represented by their single value devoid of any directional component.
In rotational motion, torque is the quantity that causes objects to rotate or change their rotational motion. Energy is essential in all forms of motion but does not have the directional attribute that defines a vector. Thus, among the two, only torque qualifies as a vector quantity.
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