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.
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.
The velocity of the center of mass is determined by taking into account all the objects and their masses and velocities. It is a weighted average velocity that accounts for the contribution of the mass and motion of each object. For two bodies with masses of 2 kg and 4 kg, moving at velocities of 2Read more
The velocity of the center of mass is determined by taking into account all the objects and their masses and velocities. It is a weighted average velocity that accounts for the contribution of the mass and motion of each object. For two bodies with masses of 2 kg and 4 kg, moving at velocities of 2 m/s and 8 m/s respectively, their center of mass velocity can be calculated by combining their individual motions proportionally to their masses. The mass with smaller magnitude contributes less to the center of mass velocity, but the larger mass will dominate and, therefore, influence it more. The average velocity is thus determined by finding the weighted average for the different velocities with their respective masses. Therefore, the center of mass velocity turns out to be 6.4 m/s, which represents the balance between the two objects and, therefore, indicates that the motion of the heavier object pulls in the system more.
The center of mass is a fundamental concept in the study of collective motion in several objects, especially in mechanics. It simplifies the analysis by focusing on a single point that behaves as if all the mass of the system were concentrated there.
The interaction between the cylinder and the surface would determine its motion when a solid cylinder rolls down a rough inclined plane. Inclined plane means that it is at an angle, causing the cylinder to experience gravitational force acting downward. The gravitational force can be divided into twRead more
The interaction between the cylinder and the surface would determine its motion when a solid cylinder rolls down a rough inclined plane. Inclined plane means that it is at an angle, causing the cylinder to experience gravitational force acting downward. The gravitational force can be divided into two: one parallel to the incline, which will push the cylinder down, and the other perpendicular to the incline, which will push the cylinder against the surface.
It therefore requires friction forces. The force of friction happens at the contact point between the cylinder and the incline where it prevents slippage. That torque is precisely what makes rolling possible as it moves down a slope. However, this movement happens in the direction that allows it to contribute to the roll.
However, this friction force also acts as a hindrance. It counteracts the motion caused by the gravitational component along the incline, which essentially prevents the translational movement of the cylinder. Thus, even though friction is facilitating rotation, it simultaneously hinders the acceleration of the center of mass of the cylinder down the incline, thus maintaining the balance between the rotational and translational dynamics.
To calculate the moment of inertia of a system consisting of four point masses arranged at the corners of a square, we start by visualizing the square with each side measuring l . The four point masses, each of mass m, are positioned at the corners of the square, designated as points A, B, C, and D.Read more
To calculate the moment of inertia of a system consisting of four point masses arranged at the corners of a square, we start by visualizing the square with each side measuring l . The four point masses, each of mass m, are positioned at the corners of the square, designated as points A, B, C, and D.
To find the moment of inertia about an axis that passes through the center of the square, we need to determine the distance of each mass from this central axis. The center of the square can be identified as the midpoint of the lines connecting the midpoints of opposite sides.
Hence using the properties of geometry, the distances from the square’s center toward where the masses have been placed, to each and all of the vertices are equal in length. When a point mass is concerned with the moment of inertia, all that matters to determine it would be the square of the mass’s distance away from the rotational axis.
Since all four masses are the same, we can sum up their individual contributions to obtain the total moment of inertia. The result will be a moment of inertia that captures the mass distribution relative to the axis of rotation, so that we get the final moment of inertia for the system. Thus, the answer to the question is 2ml².
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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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
Two bodies of masses 2 kg and 4 kg are moving with velocities 2 m/s respectively. What is velocity of their centre of mass?
The velocity of the center of mass is determined by taking into account all the objects and their masses and velocities. It is a weighted average velocity that accounts for the contribution of the mass and motion of each object. For two bodies with masses of 2 kg and 4 kg, moving at velocities of 2Read more
The velocity of the center of mass is determined by taking into account all the objects and their masses and velocities. It is a weighted average velocity that accounts for the contribution of the mass and motion of each object. For two bodies with masses of 2 kg and 4 kg, moving at velocities of 2 m/s and 8 m/s respectively, their center of mass velocity can be calculated by combining their individual motions proportionally to their masses. The mass with smaller magnitude contributes less to the center of mass velocity, but the larger mass will dominate and, therefore, influence it more. The average velocity is thus determined by finding the weighted average for the different velocities with their respective masses. Therefore, the center of mass velocity turns out to be 6.4 m/s, which represents the balance between the two objects and, therefore, indicates that the motion of the heavier object pulls in the system more.
The center of mass is a fundamental concept in the study of collective motion in several objects, especially in mechanics. It simplifies the analysis by focusing on a single point that behaves as if all the mass of the system were concentrated there.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
A solid cylinder is rolling down a rough inclined plane of inclination θ. Then
The interaction between the cylinder and the surface would determine its motion when a solid cylinder rolls down a rough inclined plane. Inclined plane means that it is at an angle, causing the cylinder to experience gravitational force acting downward. The gravitational force can be divided into twRead more
The interaction between the cylinder and the surface would determine its motion when a solid cylinder rolls down a rough inclined plane. Inclined plane means that it is at an angle, causing the cylinder to experience gravitational force acting downward. The gravitational force can be divided into two: one parallel to the incline, which will push the cylinder down, and the other perpendicular to the incline, which will push the cylinder against the surface.
It therefore requires friction forces. The force of friction happens at the contact point between the cylinder and the incline where it prevents slippage. That torque is precisely what makes rolling possible as it moves down a slope. However, this movement happens in the direction that allows it to contribute to the roll.
However, this friction force also acts as a hindrance. It counteracts the motion caused by the gravitational component along the incline, which essentially prevents the translational movement of the cylinder. Thus, even though friction is facilitating rotation, it simultaneously hinders the acceleration of the center of mass of the cylinder down the incline, thus maintaining the balance between the rotational and translational dynamics.
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See lessFour point masses, each of the value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing
To calculate the moment of inertia of a system consisting of four point masses arranged at the corners of a square, we start by visualizing the square with each side measuring l . The four point masses, each of mass m, are positioned at the corners of the square, designated as points A, B, C, and D.Read more
To calculate the moment of inertia of a system consisting of four point masses arranged at the corners of a square, we start by visualizing the square with each side measuring l . The four point masses, each of mass m, are positioned at the corners of the square, designated as points A, B, C, and D.
To find the moment of inertia about an axis that passes through the center of the square, we need to determine the distance of each mass from this central axis. The center of the square can be identified as the midpoint of the lines connecting the midpoints of opposite sides.
Hence using the properties of geometry, the distances from the square’s center toward where the masses have been placed, to each and all of the vertices are equal in length. When a point mass is concerned with the moment of inertia, all that matters to determine it would be the square of the mass’s distance away from the rotational axis.
Since all four masses are the same, we can sum up their individual contributions to obtain the total moment of inertia. The result will be a moment of inertia that captures the mass distribution relative to the axis of rotation, so that we get the final moment of inertia for the system. Thus, the answer to the question is 2ml².
See more: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
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