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Angle-free two-dimensional inelastic collision formula?

The direction of the velocities (in a center of mass system) after a collision in two (or three) dimensions will depend on the shape and size of the colliding objects (and their elastic properties). ...
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A question regarding equations of motion

v=0 after it hits the ground,SUVAT only applies when acceleration is uniform, when it hits the ground acceleration must change from 9.81 to something else, because there is now a new force acting on ...
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A question regarding equations of motion

The body's motion has two very different parts: It begins by accelerating down, until just before reaching the ground. At this point, as you noted, its velocity will be $v=-g*t$ (if the acceleration ...
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How to find time taken for a faster object to cross a slower object of same length, both moving parallel to each other in the same direction?

When solving physical problems it is essential to draw diagrams. This helps to develop a concept in your mind (especially when having no idea yet about the solution). Do this before writing down any ...
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Angle-free two-dimensional inelastic collision formula?

you can use those equations \begin{align*} &m_1\,(\mathbf v_1-\mathbf u_1)=-\lambda\,\mathbf n\\ &m_2\,(\mathbf v_2-\mathbf u_2)=\lambda\,\mathbf n\\ &\left[(\mathbf v_2-\mathbf{v}_1)+...
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How to find time taken for a faster object to cross a slower object of same length, both moving parallel to each other in the same direction?

Here you're only trying to find the time taken by this object to cover a distance equal to it's length. So, time=length/speed. Have you been given the speed and length?
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Is the deceleration a result of friction, a constant value?

Frictional force=$k$*weight=$k*m*g$ (you need gravity in there to convert mass to weight) So yes, frictional force is proportional to weight which is proportional to mass so deceleration rate is ...
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Is the deceleration a result of friction, a constant value?

There are two possible friction forces that can cause deceleration: Static friction and kinetic friction. Take the case of deceleration of a car. When you apply the brakes, the torque applied to the ...
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Is the deceleration a result of friction, a constant value?

It is generally assumed that sliding kinetic friction, $μ_k$N, is independent of speed. On the other hand, fluid friction (with the air or a liquid) does increase with an increase in speed.
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Find the equation for the angle $\theta$ in which the particle leaves the semicircle. No Friction

I don't think this is wrong. $k=0$ represents the case where the large hemisphere has zero mass, so no inertia. I think you are looking for the case where the large hemisphere is "fixed", so ...
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Does the kinetic energy theorem imply that any body on wich is exerted the same space-dependent force is equally accelerated?

$$F= m_{0}a$$ In classical mechanics, if there is the same force, then at any speed the acceleration is going to be the same. However, there is only the same change in momentum if $\int \vec{F} \cdot ...
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Does the kinetic energy theorem imply that any body on wich is exerted the same space-dependent force is equally accelerated?

We know from Newton’s second law that $\vec{F}=\frac{d\vec{p}}{dt}$. If the mass of the particle/object/body is constant, we can write $\vec{F}=m\frac{d\vec{v}}{dt}$. Rearranging the equation gives $d\...
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How do we assume the direction of $u_{\theta}$ and $u_{r}$ in polar coordinate systems?

As a rule, $\hat{u}_X$ is always pointing in the direction along which $X$ grows. It works when $X$ is a linear parameter ($x$, $z$, $r$...) as well as when it's an angular parameter ($\theta$, $\phi$....
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How do we assume the direction of $u_{\theta}$ and $u_{r}$ in polar coordinate systems?

The unit radial vector is always away from the origin. The unit tangential vector is always anti-clockwise around the origin such that $\hat{r}\times\hat{\theta}$ is out of the diagram. Not knowing ...
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Projectile with air resistance analysis

With air resistance, typically the horizontal distance is more on ascent, because it loses horizontal speed the whole way.
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Minimum energy of projectile to trigger a nuclear reaction and energy of ejectiles

Check conditions required for a nuclear reactions. Some easy ones are isotopes of hydrogen or uranium. Tupical energy per particle when reactions is detectable is about 10KeV, which is somewhere ...
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Closing speed and time needed for light to reach moving object

Your approach is not complicated at all, in fact I would suggest you solve any problem like this involving doppler shifts from basics as you did. You will get a hang of it, and if you use closing ...
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Simple harmonic motion in uniform circular motion as a projection along $x$-axis

You get different answers because, for some reason, you have taken your phase constant, $\phi$, to be $\frac{\pi}2$ whereas you should have taken it to be $–\frac{\pi}2$. $$\text{then}\ \ \ \ \ \ \ x=...
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Finding How to Transform a Plane to Reflect a Trajectory through a Given Coordinate

If we assume that during the collision, the plane only exerts a force on the ball that perpendicular to the plane itself ($\vec{F} \propto \hat{n}$), then the impulse delivered $\int \vec{F} \, dt = \...
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Recommendations for good Newtonian mechanics and kinematics books

I would like to recommend the following book: Classical Mechanics and General Properties of Matter by Satyendra Nath Maiti and Debi Prasad Raychaudhuri If you liked studying from Kleppner and ...
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Calculating the rest mass after relativistic collision

it is simply a question of terminology, the relative velocity of two observers is the velocity of one with respect to the other. This way, you do not need to appeal to a third frame that is not well-...
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Angular velocity of a particle in uniform circular motion about a general point

You can't say $dr = r d\alpha$ in this case because relative to the origin, the particle has radial velocity. You need to find the tangential component $v_t$ and use $\frac{d\alpha}{dt} r=v_t$.
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Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?

MEASUREMENTS OF THE FINITE-TIME SINGULARITY OF THE EULER DISK R. I. Leine Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland, ...
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Simple 1D Motion Problem

You are correct. Average velocity is the total distance traveled divided by the total time of travel. In other words, your journey will take the same amount of time if you travel at the average ...
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Vehicular Dynamics

the equations are $$\omega_{{3}}=\frac 12\,I_{{D}} \left( \omega_{{1}}+\omega_{{2}} \right)\\ \omega_{{4}}=I_{{G}}\omega_{{3}}\\ \omega\,R=\omega_{{1}}r\\ \omega\, \left( R+d \right) =\omega_{{2}}r $$ ...
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Calculate efficiency from discrete power, time and distance

I would recommend doing the third one: $ \frac{P_1 + P_2}{2} \times \frac{T}{M} $ for each point, then taking the average of all of them, but throwing out any where: T is greater than 2-3 seconds $...
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Can a particle move in an upward parabola fashion naturally?

Does a Parabolic orbital trajectory count? As per Kepler's first law, objects in orbit follow conic sections; Ellipses if they are moving below escape velocity, Parabolas if they are moving exactly at ...
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Can a particle move in an upward parabola fashion naturally?

You get an upward parabola, only if you have a constant acceleration upward. This could be an electric field and a charged particle. It ist part of the way an electron moves in an oscillograph ...
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