Rotation

Conservation of angular momentum states that the total angular momentum of a system remains constant in the absence of external torques. This principle is important in understanding the behavior of rotating objects in physics and plays a key role in areas such as orbital motion of planets and stars, gyroscopic stabilization, and the motion of spinning objects. It helps to predict the rotational motion of objects and systems based on initial conditions without the need to consider all the complex forces acting on them.

Assuming that angles are measured in radians, and angular velocity in radians per second (this simplifies formulae):

Radius of rotation is unrelated to angular velocity.

Linear velocity = angular velocity x radius

Centripetal acceleration = velocity squared / radius

Centripetal acceleration = (angular velocity) squared x radius

Centripetal force = mass x acceleration = mass x (angular velocity) squared x radius

The strength of the Coriolis force is influenced by the speed of the object or fluid and the latitude at which it is moving. Faster moving objects and those at higher latitudes will experience a stronger Coriolis force.

Because there is no centrifugal force. The force of circular motion is inward, thus centripetal. If you are on a car that makes a quick right turn, you feel a "centrifugal" force leftward. But in reality, it is the car making an acceleration to the center of the curve, which is to your right. What you feel is inertia, not a force.

Clockwise, top rotating to the right, and counterclockwise, top rotating to the left is only a perspective based on the position of the observer. The torque is the rotational force of the rotating object. Most often the perspective of the observer is from the driving end of a shaft facing the driven machine. The amount of torque at a given speed of the driving machine (engine or motor) is mechanically converted into work by the driven machine (generator, pump, compressor...etc.).

Whirling a hammer with a longer chain requires more force due to the increased inertia of the longer chain, making it harder to achieve the necessary speed and control to keep the hammer moving in a circular motion. The weight of the hammer at the end of a longer chain also creates a larger centripetal force that needs to be countered by the person whirling it, adding to the difficulty.

External bending moment is a force applied to a structural member that causes it to bend. It results in a combination of tensile and compressive stresses on the material of the member. External bending moments are important considerations in the design of beams and other structural elements to ensure their ability to resist bending and carry loads.

No, revolution and rotation are not the same. Revolution refers to an object's motion around an external point or axis, while rotation refers to an object spinning around its own axis. Rotation typically occurs within the object itself, while revolution involves movement around an external point or center.

Angular momentum about the axis of rotation is the moment of linear momentum about the axis. Linear momentum is mv ie product of mass and linear velocity. To get the moment of momentum we multiply mv by r, r the radius vector ie the distance right from the point to the momentum vector. So angular momentum = mv x r

But we know v = rw, so angular momentum L = mr2 x w (w-angular velocity)

mr2 is nothing but the moment of inertia of the moving body about the axis of rotation.

Hence L = I w.

No, centrifugal acceleration is not a uniform acceleration. It is a type of acceleration that occurs when an object moves in a curved path and experiences an outward force away from the center of rotation. The magnitude of centrifugal acceleration changes as the object's speed or radius of rotation changes.

The angle between the linear velocity and angular velocity of a particle moving in a circle is typically 90 degrees. This means that they are perpendicular to each other.

say mass(m) = 10 kg, radius(r) = 10 m, say friction coefficient = 0.5

force to break friction = 10 * 0.5 = 5 kgf = say 50 n

to find acceleration required to produce this force use f=m*a, shuffle to a = f / m

so a = 50 / 10 = 5 (m/s)/s, install in a = v^2 / r, so 5 = v^2 / 10,

so 10 * 5 = v^2, so sq. root 50 = v, so v = 7.07 metres / second

if friction coefficient and radius remain the same, altering the mass wont alter the velocity at breakaway point

It means how fast something rotates. Rather than taking the linear speed (meters per second, or some other common unit of speed), the angular velocity is specified in radians per second, degrees per second, revolutions (full turns) per minute, or something similar. By this definition, each part of a solid, rotating object rotates at the same angular speed.

The pendulum bob comes to rest due to air resistance and friction in the pivot point, which gradually slows down its motion. Additionally, energy is transferred from kinetic energy to other forms of energy like heat, causing the pendulum to eventually stop swinging.

The first thing you'll need is a lot of patience, as you wait for somebody to invent it.

I have to tell you, though, that there are currently no serious efforts in that direction,

by anyone reasonably comfortable with the laws of Nature and in possession of all of

his wits and faculties.

The direction of angular velocity is perpendicular to the plane in which the rotation is occurring. It follows the right-hand rule, with the thumb pointing in the direction of the axis of rotation and the fingers curling in the direction of the angular velocity.

Yes, a bar magnet can exert a torque on itself due to its own magnetic field. This torque can cause the magnet to align itself in a specific orientation, depending on the interaction between its north and south poles. If the magnet is not free to rotate, this torque can manifest itself as a force causing the magnet to move.

Both. A small driving gear and a large driven gear is a force multiplier. Whilst a large driving gear and a small driven gear is a speed multiplier

The dimension of angular momentum is kg m^2/s.

Gyromagnetic resonance in ferrites is a phenomenon where the magnetic moments of the atoms in the material precess around an applied magnetic field at a specific frequency. This resonance occurs due to the interaction between the material's electron spins and the external field and is commonly used in applications such as microwave devices and magnetic storage media.

The angular momentum of a system is not conserved when external torques are applied to the system. These torques can change the angular momentum by causing the system to rotate faster or slower or by changing the direction of its rotation.

Yes, the statement is true. Centripetal force is a force that acts towards the center of a circular path and is responsible for changing an object's direction, rather than its speed. It keeps an object moving in a circular path by constantly pulling it towards the center of the circle.