All Questions
Tagged with classical-mechanics kinematics
255 questions
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Question - Maximum range of Ballistic gunshot formula: $V_M=\sqrt{Rg}$
I have a question on physics, broke my head, saw the answer, then I see there is a formula for calculating the distance from the end of the mouth of the rocket to the finish line.
If the length of ...
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1
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76
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How fast do particles travel in space? [closed]
Does the speed of the particle in space depend on its mass? For example, if the objects are subjected to same energetic phenomena like supernova, do the heavy objects move slower than lightweight ...
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0
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Cartesian coordinate velocity and generalized coordinate velocity
use $x_k$ to denote the kth component of cartesian coordinate, and $q_k$ to denote the generalized coordinate.
Taking the derivate of $x_k(q_1,q_2,q_3,t)$ w.r.t. time, we have
$$\frac{d x_k(q_1,q_2,...
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Proving that the relative angular velocity of any particle with respect to any other particle is the same in a rigid body
Claim: The angular velocity of any point mass of a rigid body relative to any other point mass is the same, i.e., $\vec{\omega_{i,j}} = \vec{\omega}\;\,\forall{i}\,\forall{j}$, where $\vec{\omega}$ is ...
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Linearly Interpolating in a Non-Inertial Frame
I am working on an engineering task where we have a flying object which knows its height above a curved surface as well as how close it is to other flying objects. If I want to interpolate between two ...
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What does this vector represent?
Let $p$ is the position vector from the origin of frame {s} (i.e. inertial frame) to the origin of the body frame {b}. Take a look at the following picture, the vectors $\omega_b,v_b$ represent the ...
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2
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What is the physical explanation of why a $45°$ projectile angle gives the absolute maximum range? [closed]
Assuming, start and end positions are at the same height and there is no air drag.
How gravity's role plays out during flight of projectile?
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Kinematics of a 3-wheeled omnidirectional robot
Consider a 3-wheeled, omnidirectional robot (also called a kiwi drive). To see what this looks like see this YouTube video. We can control the motor speeds using a microcontroller.
Task: We have to ...
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If we know the location of object at different times, what more can we find out from it?
I'm brushing up on my physics, and I've been struggling with this problem in my head. I hope you can help.
Let's assume that we have some object/particle that only moves along a single axis ($x$). We ...
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What is the relationship between the speed of the end of the thread and the angular velocity of the spool which was pulled by the winding thread?
On a rough ground, there is a cylindrical spool of inelastic thin thread (as the picture following), the inner and outer radii are $r$ and $R$ respectively, the thin thread is wound in its inner ...
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Displacement on trip around globe?
I am tutoring in physics, specifically in kinematics and uniform acceleration, and I thought it would be fun to find the time it would take for a car to drive around the globe given an initial ...
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Finding the smallest distance between two charged particles
Problem
There's two charged particles $q$ and $q\prime$. $q$ is moving in the electric field that is created by particle $q\prime$. Find the smallest distance ($r_1$) between two particles.
Short ...
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2
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Normal reaction on a mass travelling along a curve
I've come across a set of problems in classical mechanics, where I am supposed to find the value of the normal reaction that acts on a mass, as it travels along a curve $y=f(x)$.
For example, suppose ...
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Q: How to find the height of lake given time [closed]
I'm struggling with a Kinematics homework question:
On a beautiful day you decide to go fishing with your younger brother Ben. Ben has not been fishing before so he doesn't know how to properly cast ...
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2
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Force from time and velocity
Let's say I have a goal velocity $(v)$. In $n$ amount of time $(t)$ (let's say two seconds). What is the formula for finding the amount of force I would need (not counting other forces like drag/...
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Equation of motion of a classic inverted pendulum in free fall
I was thinking in this interesting problem:
Suppose we have this inverted pendulum:
But without this control force $F$ and the system would by loose from a height $h_0$, with initial velocity $0$ ...
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Statistical Analysis of motion under central force
My question is very simple. If we were to plot the motion of a particle inside circular walls governed by a central attractive force with perfectly elastic collisions, would the statistics of the ...
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Why does the Normal reaction force vary in a straight line & curved path?
As visible from the above picture, the normal reaction force while ascending on an incline gradually decreases, however for a circular/curved path it increases. Intuitively, this seems wrong to me.
My ...
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4
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Speed resulting from tangentially applying force to solid spheres with different mass distributions
Given are two solid spheres of the same size and weight. They both have their center of mass at their geometric center.
One of them (A), however, has most of its ...
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2
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Infinite Motion from Finite Motion [closed]
By stringing an arbitrarily large number of double-reduction gears together, it is possible to create a system (assuming no gravity and no friction) where the final gear is making an arbitrarily large ...
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Newton's 1st law, applied in a manifold
A seemingly interesting question.
Newton's 1st law states that objects continue in straight lines, unless acted upon by external forces. Now consider a frictionless manifold. Since it is locally ...
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1
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Range of a projectile such that final and initial heights aren't equal [closed]
The formula for the range of a projectile is:
$$Range=\frac{v_0^2\sin2\theta}{g}$$
However, this only works when the final height is the same as the launch height. What about when it's not? I could ...
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How can the $x$-components of the frictional force and the normal force be the same for a static block on an incline? [closed]
I recently was assigned this problem as part of my homework:
"A block sits on a plane that is inclined at an angle $\theta$. Assume that the friction force is large enough to keep the block at ...
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4
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Why is a ball thrown in the air symmetrical in the time it falls
I’m having trouble with high school physics question.
The question is finding the time in the air of a ball that is thrown into the air with some initial velocity (negligible air resistance) and ...
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3
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I am moving right and rain is falling vertically down.Why should I hold umbrella at an angle?
This is related to relative velocity.I get that, from my moving frame of reference rain is making an angle.But still... it doesn't make sense to hold umbrella at an angle when rain is falling ...
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Gravitational Force & Normal Force
Imagine a moving ice-block on an extremely smooth (i.e. friction is zero) and circular, rogue planet devoid of an atmosphere. Assuming that the planet in question is far away from any (massive) object ...
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Regarding Uniform Acceleration [closed]
Please give some basic intuition or hint to solve this question. I'm getting stuck.
The star of a distant solar system explodes as a supernova. At the moment of the explosion, a
resting exploration ...
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3
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3
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Does material (density) affect falling rate of objects? [duplicate]
Suppose Galileo dropped a one-kilogram ball of cotton and one-kilogram ball of iron from the top of the Leaning Tower of Pisa, then which one will reach the ground first?
Assume that the cotton ball ...
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2
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Inclined planes and motion [closed]
A particle of mass $2\;kg$ is fired up a smooth slope of length $4 \;m$, with initial speed $10\;m/s$, inclined at an angle $30^\circ$ degrees above horizontal. What is the speed of the particle at ...
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Exact distance travelled by an object due to gravity only
I am aware of the fact that for two point masses in space, the time that it will take for them to collide is, T=$\pi \sqrt{\frac{r_i^3}{8GM}}$, where M is the sum of the 2 bodies' masses, $r_i$ is the ...
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3
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Why position of an object is unique?
Position in physics is defined as the location of an object w.r.t some reference point.
I conceptualized it as the description of the path from the reference point to the location of the object. My ...
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2
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Elasticity of spring and conservation of energy [closed]
I have a problem of one of my students mechanics homework that I am unsure on and could do with resolving by tomorrow is possible! A spring of natural length $0.5m$ is attached to the ceiling and a ...
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465
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Angular velocity to linear velocity Modern Robotics textbook
In the second to last sentence, I have no idea how $v = (2,0)$ was calculated. Can someone derive this for me in detail, or with a picture?
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4
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How to find motion equations using energy and angular momentum? [closed]
I'd really appreciate some help with an exercise.
The exercise presents a system of two bodies, $m$ and $M$. Both are connected with a weightless rope; the former is rotating (with a given initial ...
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Distance of slowing object [closed]
I have object with a given mass $m$, which is moving with the velocity $v$ and there is force $\bf F$ pushing against movement of the object.
How far will object travel until it stops and how long ...
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Equation for Work required to achieve a certain velocity [closed]
If we are trying to find the work required to get an object moving at velocity $v$, and we start with $w = f\cdot d$, we can then make the following substitutions:
substitute $f$ with ma: $w = m\cdot ...
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2
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694
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How to maintain the same initial velocity in trials with projectile motion experiment?
If I would like to experiment with projectile motion to determine the relationship of launch angle and horizontal range (for instance, I would throw a ball multiple times from a height with varying ...
user282164
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Optimum launch angle for a projectile launched from a height above the ground [closed]
If a projectile is launched from a height greater than zero and landed to a height equal to zero, is the optimum launch angle that gives the greatest horizontal range still $45$ degrees or not?
I know ...
user282164
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1
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Finding the angle required to hit a stationary target [closed]
Ignoring air resistace, I have that the height of our canon is $8.2$m and the height of the target is $6.34$m. And that our initial veocity $v_0=18$m/s. I have to determine a way to find the angle ...
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1
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Tilting a water glass so that you can run faster without spilling water (counter-diabatic driving Hamiltonian)
In this paper, there is an interesting figure:
Every attempt I've made to search online to confirm whether or not waiters/waitresses actually do this, has been unsuccessful.
Is there really an ...
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2
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Direction of velocity and displacement
Do velocity and displacement always have the same direction? I know this seems like a silly question to ask, but I'm having a hard time coming up with any counter examples, and I'm not able to prove ...
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If hypothethically a car tries to go in two different directions at the same time, which direction will it end up going?
When we add two vectors(A and B), we get one resultant sum vector(C).
i.e. adding two different directions gives us one resultant direction.
So in the same way if a hypothetical car was trying to go ...
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How to decide which velocity is bigger in a collision before writing velocity of approach and velocity of separation?
My teacher said that velocity of separation is $V_1$- $V_2$ where $V_1$ is greater than $V_2$ and said same for velocity of approach. The problem is how would you determine which velocity is greater ...
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1
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Determine the velocity by a projectile motion [closed]
A snowball rolls from the roof of a large barn that has a downward slope of 20 °. The roof end is 15.0 m above the ground and the snowball has a speed of 6.00 m / s when abandoned from the roof. At ...
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Why does the radius of curvature is constant in $n$-$t$ coordinate kinematics?
Deriving the relations kinematics on an $n$-$t$ coordinate system is said that if we have a particle $A$,after differential of time $dt$ the particle moves to $A'$. Assuming a curvilinear motion, the ...
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2
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361
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Why does something thrown out of a train goes in the opposite direction?
As someone throws some thing out of the train in y direction it should move forward (in the direction of the train) in x direction, (wrt ground) as it has velocity component in the direction of moving ...
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Why does the photon in Compton Scattering have a minimum frequency/maximum wavelenght?
Using conservation of four-momentum one finds that, with respect to the angle of deviation of the photon from its original direction $\theta$, the wavelength and frequency of the emitted photon are:
$
...
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Difference between eigenvalues of the potential energy Hessian vs. "generalized" eigenvalues with respect to a kinetic energy "metric"
Simple version
Consider if we have a Lagrangian defined by
$$L(q,\dot{q}) = \frac{1}{2} g_{ij}(q) \dot{q}^i \dot{q}^j - U(q) \tag{1a}$$
where the potential energy $U(q)$ has a single minimum at $q=0$ (...
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Inertial Torque Exerted By Engine on Crankshaft
In Shigley(5th Edition), in Chapter 14. Dynamics of Reciprocating Engine ,Section 14.7 Inertia Forces,
the inertia torque exerted by the engine on the crankshaft is given as
$$
\mathbf{T}_{21}^{\...
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1
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375
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Angular acceleration of ball when falling [duplicate]
Why is it assumed that angular acceleration is 0 when a ball is midair after rolling off a surface with constant velocity?