In physics, motion is the phenomenon in which an object changes its position over time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and time. The motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame with change in time. The branch of physics describing the motion of objects without reference to its cause is kinematics; the branch studying forces and their effect on motion is dynamics.
If an object is not changing relatively to a given frame of reference, the object is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. As there is no absolute frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be in motion.Motion applies to various physical systems: to objects, bodies, matter particles, matter fields, radiation, radiation fields, radiation particles, curvature, and space-time. One can also speak of motion of images, shapes, and boundaries. So, the term motion, in general, signifies a continuous change in the positions or configuration of a physical system in space. For example, one can talk about the motion of a wave or about the motion of a quantum particle, where the configuration consists of probabilities of occupying specific positions.
The main quantity that measures the motion of a body is momentum. An object's momentum increases with the object's mass and with its velocity. The total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum. An object's motion, and thus its momentum, cannot change unless a force acts on the body.
First, I tried to model the disk-bar as a crank connecting rod, to the OA bar, and apply this:
VP = VB + ω_BP x r_P/B, where P is the contact point between the disc and OA bar.
I assumed VP = VP sin 30º i + VP cos 30º j (direction parallel to r_P/B), where r_P/B = sin 30º i + cos 30 j
This...
I just want to check if my thinking is reasonable. Since B,C and D are all dependent or fixed by the oscillator, A is the only factor to affect the amplitude of the motion at resonance or even throughout the entire process?
Let me start be making a small sketch of the problem, shown to the right.
If the range of the projectile on a still day ##R = v_{0x}T##, then on the windy day the range becomes ##R+2H = v'_{0x}T = (v_{0x}+v_w) T##.
Since the maximum height attained by the projectile ##H =...
Hello,
Apologies if this is in the wrong section, it's related to circles so I figured Geometry was the best place. I found a very good example online that explains how to determine a future position of an object undergoing uniform circular motion:
(Note that they made a mistake by writing...
Heisenberg equation of motion for operators are given by
i\hbar\frac{d\hat{A}}{dt}=i\hbar\frac{\partial \hat{A}}{\partial t}+[\hat{A},\hat{H}].
Almost always ##\frac{\partial \hat{A}}{\partial t}=0##. When that is not the case?
I was watching a video about jet engines, and it was obvious for me and for the instructor that if we compress air at high speed from the gas turbine inlet, then after multiple stages collide with the turbines blades inside, the body will move in the sense of difference in velocity, so forward...
Of potential and kinetic energy in their various forms, in their own reference frames, which involve motion? Heat, light, nuclear, kinetic, etc., seem to involve motion. Does potential energy, in any way whatsoever, involve motion? Thermal does. Does nuclear energy involve motion? Seems to...
53 rpm equals 5.55 rad/sec
multiply 5.55 by 2pi to get angular velocity of 34.8717
Is the answer 34.8717?
What should I have done to more accurately solve the problem with a better understanding?
What other steps should I take when solving similar problems?
and lastly,
Is the mass relevant...
So first I find the energy using the eqn (1/2)kA^2. Since there are two springs with the same k I multiply it by two to get kA^2. Energy I get is 2.0475,
Now I use E=(1/2)m(wA)^2 to find mass. Again since there are two springs I use E=m(wA)^2.
m=E/(wA)^2. w=(2(pi))/T btw.
I get the answer of...
I once naively think that the speed of light is also a constant in a medium in all inertial frames which is not the case. I tried to derive the result yet there is a discrepancy from the results I read in some articles.
For example, from [Link to unpublished paper redacted by the Mentors], the...
I'm trying to solve this problem using an rtz coordinate system, and Newtons second law. I know that mar = (m(v)2)/r. I'm failing to understand how mg and the drag force affects the solution and how I would set it up. I know if it was at the bottom of the circle that mg would be added to the...
in my head this is just a silly problem in which i need to determine the ↓ force (weight) and the ↑force (archimedes bouyant force) and then the difference must be the drag force ↑ (the force that involves velocity) but i can't get any sense out of this answer
how is possible for the sphere to...
Hello. Can someone tell me what area of phisics should I study to better understand this exercise( I ve been looking at kinematics since it asks for the velocity but I can't seem to find where it talks about different points like this) and also what should I do to solve this exercise please?
A...
So for this problem the solution used Cartesian coordinates but I was wondering wouldn’t it be easier to use Normal and tangential coordinate because the bar is undergoing centripetal motion? Also on the right diagram shouldn’t the acceleration be down and not up. The reason I think that is...
So I have questions on two separate questions. The first question is about the fbd of the plate attached to the pin. How can there be an Ax since there’s no other force in the horizontal direction wouldn’t the plate start moving on the x-direction due to imbalanced forces.
Second question about...
A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R. A smooth horizontal groove AB of length L(<<R) is made on the surface of the table. The groove makes an angle θ with the radius OA of the circle in which the...
Let me imagine myself standing on the Earth with my arm in the resting position perpendicular to the ground. Now if I decide to raise my right arm by 90 degrees, now that it is parallel to the ground. I have shifted my center of mass in this process. But the center of mass will not accelerate...
a) When the system is in motion for the first time, the force causing ##M## to move is contact force with ##m## so:
$$\Sigma F=M.a$$
$$N \sin \alpha=M.a$$
$$mg \cos \alpha \sin \alpha =M.a$$
$$a=\frac{mg \cos \alpha \sin \alpha}{M}$$
Is that correct?
b) Is acceleration of ##m## the same as...
Hi,
I have to find the motion of a particles ##(x,y,z)##. However, I'm not sure where to begin.
Is it correct to split the problem and first find what's the motion in the x direction then y and z.
For exemple,
##m \frac{d^2x}{dt^2} = -kv_{0x} + qv_{0x}B sin 90 ##
##m\int\int...
I'm having a bit of a problem with some projectile motion. The standard motion is not a problem, but how to I compensate for a projectile that is rotating or tumbling backwards (nose over tail) at a significant rate of speed. The Tumble rotation is about 50 degrees/second on a cylindrical...
My doubt is with Method 2 of the given example in KK.
I'm unable to understand why the torque around A (where we have chosen a coordinate system at A) becomes zero due to the R x F in z direction with a minus sign {Photo Attached}
I have tried to reason out that one way to formulate that term...
Summary:: I have come across a situation where I seem to get different equations of motion for an oscillating system. Please do help me find out where I went wrong.
*I am not asking how to solve the problem*
I am going to consider 4 parts of the cylinder's motion, as listed below. (There is...
Summary:: What are the Equations of motion for a free damped 2-Dof systrem?
Hello,
I am required to calculate the equations of motion for a 2-dof system as shown in the attached file. The system is undergoing free damped vibrations. I have found the equations of motion for no damping but i...
In Robert Wald's General Relativity textbook page 64 reads:
__________________________
In prerelativity physics, the electric field ##\vec{E}## and magnetic field ##\vec{B}## each are spatial vectors. In special relativity these fields are combined into a single spacetime tensor field ##F_{ab}##...
I do not agree, this is bullocks. We can simply set up position vector of ##\vec A(t)## and ##\vec B(t)## with respect to the fixed center of the carousel, their relative velocity is simply ##\frac{d (A-B)}{dt}## or ##\frac{d (B-A)}{dt}##
Since this is a pretty popular book, I am wondering if I...
mball = 2 kg, mputty = 0.05 kg, L = 0.5 m, v = 3m/s
a) Moment of inertia : I = (2mball + mputty ). ¼ L^2 = 0.253125 kg.m^2
Linitial = Lfinal => mputty. v. r = I.ω => ω = (4.mputty.v.r) / I = 0.148 rad/s
b) K initial = 1/2 m v^2 = 0.225 J
K final = 1/2 Iω^2 = 2.85.10^(-3) J => Kfinal /...
Assuming zero spring mass and zero friction,
At the greatest value of x, the loss in gravitational potential energy should equal the loss in elastic potential energy.
so I did
(1/2)kx^2=mgx
to isolate x in the formula,
x=(2mg)/k
then I plugged in my values so:
(2*13.6*9.81)/8.8= 30.3218...
First I figured out the normal force being exerted on the car using the equation above.
Cos(40°)*(1050*9.8) = 7883N
Next, I tried to find out the horizontal component of the normal force by doing:
Cos(50) * 7883 = 5067N
I figured out the angle by using certain geometrical properties.
Next, I...
just something i think about, maybe it difficult to answer.
i know, from study, that any observer moving along his world-line - in any state of motion - will not himself notice any difference to the rate which time passes for him. example: his heart-rate will feel normal (well, so long as he...
I was pondering my practice of talking about circular motion in the horizontal direction and the vertical direction. But I'd often would see in books, notes, and the internet that we assume constant velocity for the vertical case. However, when one thinks about the forces at different points in...
total time: t = 36 mins = 0.6h = t1 + t2
=> t2 = t - t1 = 0.6h - 0.1h = 0.5h
Vmax = a1 x t1
Vat C = Vmax + a2t2
substitute Vmax in Vat C we have : 0 = a1 x 0.1h + (-600 km/h²) x 0.5h => a1 = 3000km/h²
Vmax = a1 x t1 = 3000 x 0.1 = 300km/h
I check the result by:
x1 = ½ a1 t1² = ½ . (3000)...
I know that the answer is 0 J (no NET work was done) because there is symmetry to the problem and this symmetry comes from the fact that the direction of force changes, BUT I don’t know why the force changes (I have an idea; TBD below in #4). When I did this problem I thought I could find the...
1)Find the range of the gun when the muzzle speed is 400m/s and the elevation 24.5°
- I tried to find " Time " via t= [v-u]/a by substituting it through cos-->
t= ( 0- [400cos24.5] )/-10 and got [ 36.39 ].
Which I then substituted in S=ut---> S= ( 400cos24.5 ) x 36.39=13245.3.
[ the answer...
Question 1:
I believe that the ratio would be b. 8:1 because by combining the formula for kinetic energy and momentum the expression Ek=p^2/2m can be obtained.
Thus, for a body of mass 2kg with twice the momentum:
Ek=2^2/2*2=1
For a body of mass 4kg with half the momentum:
Ek=1^2/2*4=1/8...
In the figure assume the "ceiling" moves with motion ##Y(t)##, i.e. it is a point support.
Applying Newton's law in the vertical direction
##T(y).\hat{y}=\rho y[g+\frac{d^{2}Y}{dt^{2}}]##
If ##\theta## is the angle between ##T## and ##\hat{y}## that means ##|T|\cos\theta=\rho...
Suppose a particle is moving around a circular track of radius R at speed v. To bend around a circle some agency has to exert an acceleration towards the center of the circle. I analyze the forces acting on the particle, its weight and the normal force and there is no acceleration in the...
I have trouble solving this problem any help would be appreciated.Problem statement
##J=\frac{mr^2}{2}##
a) Determine the motion of yoyos for ##n=1,2,3##
The case for ##n=1## is simple, however, I am having trouble with ##n=2## and ##n=3##.
for ##n=2## I started by drawing all the forces...
Hey everyone, where can I learn fairly rigorousoly about continuum mechanics and specifically about how to map between motions in the configuration space ##\mathcal{C}## and motions in the shape space ##\mathcal{C} / SO(3)##? I would like to model the general motion of deformable bodies with...
Consider the Schrödinger equation for a free particle:
\begin{equation}
-\frac{\hbar^2}{2m} \partial_i^2\psi = i\hbar\partial_t \psi.
\end{equation}
Let us be interested in the motion of a free particle in quantum mechanics. We say ok, we have a solution to the Schrödinger equation for a...
So what I did was made the two equations equal each other. A lot of stuff cancels out and I end up with x=-vt. My issue is that t isn't given and I am not entirely sure how to get it. I don't think taking the partitial derivative of time will be any help nor the partial derivative of...
APPROACH 1 (correct):
Height above ground = 3 - (v+u)/2 * t
= 3 - 18.263/2 * 0.25
= 0.717 m
-----------------------------------------------------
APPROACH 2 (incorrect):
Let d be the height from the ground when he is stopped by the cushion.
PE loss = Work done against motion by cushion
mgh =...
Hi,
I have a particle on a parabolic surface $$y = Ax^2$$ and I have to show that the frequency is $$\omega = \sqrt{2Ag}$$
I don't know how to deal with a parabola. I don't think I can use the polar coordinates like a circle.
I don't see how to start this problem and in which coordinates...
Let:
##x## = horizontal distance from person to tree
##h_t## = height where arrow hits the coconut (measured from ground)
##h_o## = height of monkey
##u## = initial speed of arrow
##\theta = 35^0##
##t = 1~ \text{s}##
Vertical displacement of coconut until it is hit:
$$h_t - h_o = -\frac{1}{2}...
Hi,
how can I calculate the impact force in case when some object is in uniform circular motion and then suddenly hits the target. For example consider lawn mower's blade hitting stone or drum woodchipper's blade hitting branch. Both blades are already moving at full speed when they hit the...
So since V(cap) + V(ind)=0 then Q/C + L dI/dt=0
Now since I=dQ/dt, I can replace dI/dt with d^2Q/dt^2 resulting in Q/C + L d^2Q/dt^2 =0
Now L d^2Q/dt^2 looks like a harmonic motion thing I can solve, where w^2=L. This means I can find w. I get 0.0005385.
Now my issue is using this w gives the...