It is important to keep in mind that there are two distinct conventional approaches to discussing forces and inertial motion. The Newtonian method treats gravity as a force, while ideas from General Relativity view gravity as a result of spacetime’s geometric curvature through which objects move. These were the initial laws governing the forces impacting […]

# Category: Newtonian mechanics

## Methods for determining mass moment of inertia

To find moment of inertia you just sum distance squared times mass of each particle I = ∑ i r i 2 m i The above equation works well in discrete case, but in continuous case the sum becomes integral (1) I = ∭ V r 2 d m where V is the volume that […]

## Calculating distance using acceleration and time

For instance, consider the values $a=5$, $b=0.1$, and $c=0.2$ (https://www.desmos.com/calculator/7n88v2vafp). In Solution 2, the two differential equations need to be solved numerically, such as with a MATLAB program. The equations are: $$frac{d}{dt}v(t) = frac{p}{v(t)} – b(v(t))^2 + c$$ $$frac{d}{dt}x(t) = v(t)$$ The simulation results show the initial conditions: $v(0) = 10/3.6$ [m/s] and $x(0) = […]

## Angular Momentum Conservation Principle Reworded

The question highlights the definition of angular momentum as the cross product of position and linear momentum. The physics behind it involves reducing moment of inertia, resulting in an increase in angular velocity due to the conservation of angular momentum. Therefore, when the person pulled their arms in, the chair spun faster. Question: As a […]

## Collision characterized by perfect elasticity

The collision process exhibits high elasticity as most of the incident kinetic energy transforms into elastic energy and is returned as kinetic energy. During collision, the transfer of “force” from the first object to the second is not actual, but momentum or kinetic energy can be considered as being transferred. Solution 1: The degree of […]

## The Measurement of Work Done

The exertion of force on an object results in its movement over a distance, signifying the accomplishment of work. In essence, this explanation emphasizes that the total work done on an object can be determined by summing up the work performed by each individual force that acts on it, with consideration given to the chosen […]

## Maximum height for a fall that can be survived

Andrew Grimm referred to a 1987 study that is widely known to suggest that cats not only survive terminal velocity, but also have a higher chance of survival over shorter distances. The Straight Dope mentioned the cats’ falling distance, including the terminal velocity. However, The Straight Dope also noted that the statistics on cats surviving […]

## Origin of the Definition of Newton’s Second Law: Tracing its Roots

By defining force as the time-derivative of momentum, the units of momentum (mass times velocity) divided by the units of time can be obtained. The rate of change of momentum is plotted on the y-axis, while on the x-axis, it is easy to understand that using two toy arrows will provide twice the value of […]

## Understanding Internal Forces: A Guide to Calculating Them

The definition of systems can be modified, leading to a change in the interpretation of internal and external forces. If we view planet Earth as a system, would the events occurring within this system, such as moving cars, be considered as internal forces? If there is a change in momentum within the system, it is […]

## Calculating the Moment of Inertia: A Guide

(1-v) boldsymbol{B} + u,v,boldsymbol{C} $$ The area element inside the triangle is $$ {rm d},{rm area}(i) = frac{partial {rm pos}}{partial u} times frac{partial {rm pos}}{partial v} ; {rm d}u ,{rm d}v = u left( boldsymbol{A} times boldsymbol{B} + boldsymbol{B} times boldsymbol{C} + boldsymbol{C} times boldsymbol{A} right) {rm d}u ,{rm d}v $$ the integral of which […]