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Rotation

Classical mechanics doesn't just describe how an object's position behaves under external influences, but also how its orientation behaves. Using the same principles found in Newtonian mechanics, laws and relations governing rotation can also be derived. Please direct all your questions about moments of inertia, angular velocity, angular momentum, centripetal force, centrifugal force, torque, and spin here.

645 Questions

What is angular acceleration?

Angular acceleration is the rate of change of angular velocity with respect to time. It measures how quickly an object's angular velocity is changing as it rotates around an axis. It is typically denoted by the symbol alpha.

What are the Ways of application of centripetal force and centrifugal force?

Centripetal force is applied towards the center of a rotating object, keeping it in a circular path. This force is used in circular motion, like in a swinging ball on a string or a car making a turn. Centrifugal force is a perceived outward force in a rotating system that seems to push objects away from the center. It is often referred to as a "fictitious" force and can be observed in situations like a spinning amusement park ride or a car taking a sharp turn.

Can a small force produce a greater torque than a large force?

Yes, a small force applied at a greater distance from the pivot point can produce a greater torque than a large force applied closer to the pivot point. This is because torque is the product of force and distance.

What happens to the angular speed of a star as it shrinks?

As a star shrinks, its angular speed typically increases due to the conservation of angular momentum. This means that as the star's radius decreases, its rotation rate speeds up in order to conserve the total angular momentum of the system.

What would happen if there was no inertia?

Without inertia, objects would not resist changes in their motion. This means that any force applied to an object would instantly change its speed or direction, making it impossible to move or control objects effectively. The concept of momentum would not exist, leading to chaotic and unpredictable movements of objects.

What is the equation for the coriolis effect?

The equation for the Coriolis effect is ( F_c = 2m \times v \times \Omega \sin(\theta) ), where ( F_c ) is the Coriolis force, ( m ) is the mass of the moving object, ( v ) is the velocity of the object, ( \Omega ) is the angular velocity of the rotating frame of reference, and ( \theta ) is the angle between the velocity vector and the axis of rotation.

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 ms along the direction r you j what is its angular momentum relative to the point 05 meters?

The angular momentum of the particle relative to the point is given by the formula, L = m * r * v * sin(θ), where m is the mass (2 kg), r is the distance (0.5 m), v is the speed (3 m/s), and θ is the angle between the position vector and the velocity vector (90 degrees as they are perpendicular). Substituting the values, the angular momentum L = 2 kg * 0.5 m * 3 m/s * sin(90°). Finally, L = 3 kg m²/s.

What can the rotational force do?

Rotational force, also known as torque, can change the rotation of an object, accelerate or decelerate its angular velocity, and cause it to rotate around a specific axis. It is responsible for the motion of objects like wheels, gears, and propellers.

Torque vs moment?

In physics, torque and moment are essentially the same thing. Both terms refer to a measure of the rotational effect that a force has, with torque typically used in engineering and mechanics, while moment is more commonly used in physics and mathematics. They both involve a force applied at a distance from a pivot point, resulting in a tendency to cause angular acceleration.

How can inertia be overcome?

Inertia can be overcome by applying an external force to an object. The greater the force applied, the quicker the object's inertia can be overcome. Once the external force is greater than the object's inertia, it will begin to move or change its speed/direction.

What is the angular velocity of the minute hand?

The angular velocity of the minute hand can be calculated as 2π radians divided by the time it takes to complete one full revolution, which is 60 minutes. Therefore, the angular velocity of the minute hand is π/30 radians per minute.

At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis People sit in seats facing the axis their backs against the outer wall At one instant the oute?

The description seems to be about a ride commonly known as "the scrambler" or "the rotor". This ride has cylindrical chambers that spin around a central axis, with people sitting in seats facing the axis and their backs against the outer wall. It creates a centrifugal force that pushes riders against the wall as the chambers rotate.

Define angular speed?

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity.[1]

One revolution is equal to 2π radians, hence[1][2]

where

ω is the angular frequency or angular speed (measured in radians per second), T is the period (measured in seconds), f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν),

How to convert Angular velocity to velocity?

To convert angular velocity to linear velocity, you can use the formula: linear velocity = angular velocity * radius. This formula accounts for the fact that linear velocity is the distance traveled per unit time (similar to speed), while angular velocity is the rate of change of angular position. By multiplying angular velocity by the radius of the rotating object, you can calculate the linear velocity at the point of interest on that object.

What is an example in which the net force acting on a object is zero and the net torque is nonzero?

One example is a beam in rotational equilibrium supported by two forces at opposite ends. If the forces are equal in magnitude and opposite in direction, the net force is zero, but the torques produced by these forces would be unequal, resulting in a non-zero net torque that maintains rotational equilibrium.

What is a displacement can?

A displacement can is a cylindrical device used to accurately measure the volume of liquids or gases. It works by displacing fluid within a chamber, and the volume displayed on its calibrated scale is directly proportional to the amount of fluid displaced. Displacement cans are commonly used in laboratories and industries for precise volume measurement.

What is angular momentum?

Angular momentum is a measure of an object's rotational motion, determined by the mass of the object, its angular velocity (rate of rotation), and the distribution of mass around its axis of rotation. It is a vector quantity, with both magnitude and direction, and is conserved in the absence of external torques.

A wheel has a radius of 4.3 m How far path length does a point on the circumference travel if the wheel is rotated through angles of 30 30 rad and 30 rev respectively?

The diameter (i.e. the length of the outside) of the wheel is 4.3 meters times Pi (3.14) or abut 13.5 meters.

Circumference = 4.3 m x Pi = 4.3 x 3.14 = 13.5m

For a 30 degree rotation, the wagon will have moved forward a fraction of the wheel's circumference that is equal to the percentage of the wheel thatis represented by 30degrees. Since the circumference is represented by 360 dgrees, this percetange is 30/360.

Distance moved = (percentage of circumference represented by 30 degrees)x(circumference)

= (30 degrees/360 degrees)x(13.5m) = 1.125m or 1-1/8m

For a 30 rad rotation (rad=radians) , the wagon will have moved forward a multiple of the wheel's circumference that is equal to the multiple that is represented by 30radians. Since the there 2 times Pi radians per 360 degrees, there are 2xPi radians per circumference.

Thirty radians (in terms of circumference) = (number of radians)/radians per one circumference) =(30 radians)(1 circumference/2 x Pi radians) =15/Pi circumferences

Distance moved = (multiple of circumference represented by 30 radians)x(circumference)

= (15/Pi circumferences)x(4.3m x Pi) = 15x4.3 m = 64.5m

For 30 revolutions, the wagon will have moved forward 30 times the wheel's circumference because one revolution is equal to one circumference.

Thirty revolutions = number of revolutions x (number of circumferences/revolution) = 30 rev x (1 rev/1 circumference) = 30 circumferences

Distance moved = (30 circumferences)x(13.5m) = 405m

Centrifugal force increases with?

Centrifugal force increases with increasing speed and radius of rotation. The faster an object moves in a circular path or the larger the radius of rotation, the stronger the centrifugal force acting on the object.

What are the 3 ways you can change torque?

You can change torque by adjusting the force applied, changing the distance between the force and the pivot point, or altering the angle at which the force is applied relative to the pivot point.

Why does earth spin counter clockwise?

Almost all of the material that formed the Solar system revolved around the Sun in one direction. This represents the conservation of angular momentum when the material contracted to form the Sun and its planetary disk. Since then, collisions and localized gravity have created exceptions to the general counter-clockwise rule (Venus spins slowly clockwise on its axis).

The Earth rotates (spins) on its axis counter-clockwise, and orbits the Sun counter-clockwise as well, as viewed from the North Pole of the Earth or Sun. These are arbitrary concepts of "above" and "below" the plane of the Solar System. The Moon also revolves around the Earth counter-clockwise.

Does using an extension on a torque wrench change the ability to achieve the desired torque value?

If you are just sticking a piece of pipe on the handle so you (as the user) can apply more force to the tool, no, it won't change the ability to get a desired torque on a fastner. And adding an extension between the socket and the drive head of the wrench (a so-called socket extension) to extend the reach of the tool won't negatively affect the performance of the tool, either. The tool must be used properly in either case to get accurate results, but the torque wrench's ability to deliver correct results in accordance with the settings on it won't be diminished. If the tool is the so-called beam-type torque wrench, again, no, you shouldn't have a problem as long as you work carefully.

How angular momentum is equals to kgms?

Angular momentum is calculated as the product of a rotating object's moment of inertia (I) and its angular velocity (ω). The units of angular momentum are kg m^2/s, which is the same as the units for moment of inertia multiplied by angular velocity (kg m^2 * 1/s). This relationship is based on the principles of rotational motion and conservation of angular momentum.

Centrifugal force is the force that?

Centrifugal force is the outward force of a rotating object. The opposite force is the

centripetal force which maintains the object in it's rotational position. In the case of

an orbiting satellite it's rotational speed (revolutions per time period) creates the

centrifugal force required to overcome the gravitational pull (centripetal force) of the

body it is orbiting.

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The first answer is a neat, tidy, well-written summary of perhaps the most popular

misconception in all of elementary Physics. Centrifugal force is a concept made up

to account for the sensation of force that we perceive when we move in a curve.

There need not be any outward force on a rotating object, and in general there is none.

Centripetal force is real. It's the force required to bend the path of a moving abject

away from a straight line. There is no outward force on an orbiting satellite. No force

is required, and none exists, to 'overcome' the centripetal gravitational pull. In fact,

if there were a force that overcame the gravitational centripetal force, then the

forces on the satellite would sum to zero and it would travel in a straight line.