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The minimum speed required for an object to complete a vertical circle is derived to be (rg)^0.5 at the top of the circle, where r is the radius and g is the acceleration due to gravity Though average speed over a finite interval of time is greater or equal to the magnitude of the average velocity, instantaneous speed at an instant is equal to the magnitude of the instantaneous velocity at that instant If the object has a speed lower than this at the top, it will not have enough centripetal force to stay on the circular path and will fall off

The discussion emphasizes that as the object moves past the top. To determine the maximum height, the vertical component of the initial velocity must be considered, and the appropriate. The viscous force within a fluid will depend on the velocity gradient (aka shear rate) within the fluid

That does not mean that the viscosity is a function of velocity

Viscosity is the ratio between the viscous force and the shear rate As long as viscous force and shear rate have a linear relationship, viscosity will have a single fixed value. I heard it would be possible to have zero instantanous velocity & non zero acceleration (i know the opposite situation where there is velocity (constant), but zero acceleration). The discussion centers on the relationship between the exit velocity of gas and the diameter of a hole in a pressurized container

Initially, it was suggested that the exit velocity increases with larger hole diameters based on bernoulli's principle and the continuity equation However, further analysis revealed that the exit velocity is primarily determined by the pressure difference between. Since the phase velocity is linear in , , the group velocity is an average of all the phase velocities in the wave pocket This turns out true in the simplest case which wave pocket contains two waves with wave vectors and.

To find angular velocity (ω) from torque (τ), the relationship τ = iα is used, where i is the moment of inertia and α is angular acceleration

Angular acceleration can be expressed as α = dω/dt, leading to the equation dω/dt = τ/i By integrating this equation over time, one can determine the change in angular velocity, taking into account the initial angular velocity Velocity is fundamentally a vector quantity, possessing both magnitude and direction, while speed is a scalar representing only magnitude In the context of the suvat equations, the symbol 'v' can represent either velocity or speed depending on the notation used

Typically, an arrow indicates a vector Phase velocity and wave velocity are numerically equivalent, defined as ω/k, but conceptually they can represent different aspects of wave behavior While both terms describe the speed of wave propagation, they are not always interchangeable, especially in dispersive media where group velocity and phase velocity can differ Group velocity, which is the speed at which information travels, is.

The calculated initial velocity is approximately 27.586 m/s, which is confirmed as reasonable by other participants

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