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.
How can I calculate the trajectory of an object knowing the initial conditions and the function F(x,y)?
For example, a object orbiting a planet or two electric charges orbiting each other.
Homework Statement
Solve problem 8.1, but using force and torque rather than conservation of energy. (Image of 8.1 attached)
Homework Equations
T = f x d
f = ma
The Attempt at a Solution
I think I might have to find the torque on the disk, which I’m guessing would be 2mgr - mgr, but I’m...
I have just begun my journey in Classical Mechanics with the book "An Introduction to Mechanics" by Kleppner and Kolenkow. I find myself stuck at Newton's first law. The book presents Newton's first law as follows:
"Newton's first law is an assertion that inertial frames exist."
The book also...
$$\tiny{243.13.01.18}$$
$\textsf{The following equations each describe the motion of a particle.}\\$
$\textsf{For which path is the particle's velocity vector always orthogonal to its acceleration vector?}$
$\begin{align*} \displaystyle
(1) r(t)&=t^8i+t^5j\\
(2) r(t)&=\cos(8t)i+\sin(2t)j\\
(3)...
<Moderator's note: Removed template prior to moving it from Homework.>
I am looking at centripetal acceleration, and I know that even at a constant speed the object is acceleration because its velocity is changing. But I don't understand how it is changing, like when is it negative and when is...
Vibrations - Modelling system, equation of motion
Hi,
In the first question (question 4) in the attached file, how would you go about modelling the system and finding the equation of motion? All those masses are confusing me, I don't even know where to start.
I don't know whether the angle...
I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe...
Homework Statement
I'm not asking for a full on solution to my question, but instead wanted to know what was the difference in these two questions. So, here are the two questions
1) A space station of radius 90 m is rotating to simulate a gravitational field.
What is the period of the space...
Homework Statement
The maximum speed with which a car can take a circular turn of radius R is v. The maximum speed with which the same car, under the same conditions, can take a circular turn of radius 2R is
A. 2v
B. v√2
C. 4v
D. 2v√2
Homework Equations
v = (2πr)/T
The Attempt at a Solution...
Homework Statement
The following question involves a torque acting on a particle in rotational motion. It provides practice with the various equations for angular velocity, torque etc A particle of mass ##m## initially has position...
Homework Statement
Homework Equations
F = mv^2/R
The Attempt at a Solution
I got that T1max = T2max because when i plugged into my formula for centripetal force, i get that both ropes end up with mv^2/R which means they are equal everywhere... Is this correct?
Homework Statement
Hello! I have 2 bodies initially at rest, of equal masses with the distance between them a and coordinates ##(a cos(\theta),a sin(\theta))## and ##(-a cos(\theta),-a sin(\theta))##. If we denote ##a_x## and ##a_y## the horizontal and vertical distance between them they...
Homework Statement
The differential equation of motion for the simple pendulum can be shown to be
##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released
from rest at θ=60deg, determine the time required for the pendulum to reach the position
θ=0deg. Use Δt=0.10s, and...
Homework Statement
Assume the roller coaster cart rolls along the curved track from point A to point C under the influence of gravity. Assume the friction between the cart and track is negligible. What would be the direction of the carts acceleration at point A? (The question in the image does...
Homework Statement
A child sitting in a tree throws his apple core from where he is perched (4.0m high) with a velocity of 5.0 m/s [35 degrees above horizontal], and it hits the ground right next to his friend.
A) How long is it before the apple core hits the ground?
B) How far from the base...
Homework Statement
Where does T2cos(theta) come from ? Isn't mv^2/R the centripetal force which is the tension of rope 2?
Homework Equations
Fc = mv^2/R
3. Solution
Wait! The horizontal component of the circle is the centripetal force? So that part is mv^2/R?
I got confused and thought...
Assume we shoot a space shuttle of mass m to space. We know it affects the Earth's mass M by decreasing it to M2 = M-m. Assume that the gas pillar that the space shuttle shoots has no effects on earth, what would be the theoretical effects on kinetic energy, momentum and velocity of the Earth by...
Is there any way to synchronize two clocks already in relative inertial motion? If so, how? And I am not sure exactly what “synchronize” would mean in that context. Maybe it would mean that their readings, or at least their running rates, would match when their relative motion was stopped? There...
How are we able to move trough the aire if the air exerts a force equal to the friction we use to push us through air?
I´ve had this problem in my mind since some days now. I did this picture:
url: https://www.kn3.net/60DAC45480AJPG.html
I found this interesting problem on the internet, but I think there is not enough infromation to solve.
"At the 1998 Punkin Chunkin World Championship, a pneumatically-driven device called the "Aludium Q36 Pumpkin Modulator" was able to project a 3.6-4.5 kg (8-10 pound) pumpkin intact for a...
I am very confused about angular velocity ω and why its used in simple harmonic motion. ω is described as θ/τ but when it comes to masses on springs, there is no angle - it is zero. Angular velocity comes from circular motion but the motion of SHM is not circular. My confusion is even greater...
Homework Statement
You hold a small ice cube near the top edge of a hemispherical bowl of radius 100 mm. You release the cube from rest. What is the magnitude of its acceleration at the instant it reaches the bottom of the bowl? Ignore friction.
Homework Equations
ΣF = ma
Fg = mg
The Attempt...
I am finishing up a lab write up for conservation of energy, where we launched a projectile into the air and measured the initial velocity and height of the projectile. ( 10 trials)
One of my questions asks if I wanted the ball (projectile) to travel twice as high, how much faster would it have...
Hello, I have a doubt about the Complete Set of commuting observables (CSCO) in the cases when there are a magnetic field ##B## in z.
The statement is find the constant of motion and CSCO for a particle of mass m and spin 1/2, not necessary a electron or any atomic particle.
I know that the...
Homework Statement
A hunter aims a high velocity semi-automatic rifle at a moose that is 500.0 m away in a direct line of sight. The moose stands 40.0 m below the horizontal in a depression with a bog at the bottom. The muzzle velocity is 2500.0 feet per second and the sight on the rifle is...
Homework Statement
The speed of the pendulum bob remains constant
as it travels around the circle
(a) Over one complete circle, how
much work does the tension force F do on the bob? (i) A positive amount; (ii) a negative
amount; (iii) zero.
(b) Over one complete circle, how much work does...
Homework Statement
Homework Equations
## v = r \omega##
The Attempt at a Solution
Velocity of point B= ##v_B = 4 \times \omega = 4 ## m/s
Since the separation between B and C is constrained to be a constant, Velocity of B along rod = Velocity of C along the rod
## \Rightarrow v_B \cos \theta...
1. Homework Statement
You have two masses moving across a frictionless surface, yet there is friction between the two masses. Mass 2 is on top of Mass 1 A force is applied to m1 which causes It to accelerate at 6 m/s2 and the friction between the two masses causes m2 to accelerate at 4 m/s2...
< Mentor Note -- thread moved to HH from the technical physics forums (because of a forum issue), so no HH Template is shown >
There was a huge explosion, one small piece of debris was launched upward at v=5.3 km/s. Calculate its maximum altitude.
a) Develop an expression for the maximum...
Homework Statement
A football receiver running straight downfield at 5.5m/s is 10m in front of the quarterback when a pass is thrown downfield at 25 degrees above the horizon. If the receiver never changes speed and the ball is caught at the same height from which it was thrown find initial...
Hello everybody, I Am Meaningless and I had this doubt when I was reading some illustrations based on questions in Particle mechanics.
So the Question was,
A particle is attracted by a force to a fixed point varying inversely as (distance)^n. If the velocity acquired in falling from an...
Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible mass. Block A is placed on a very rough tabletop as shown below, and block B hangs over the edge of the table. The tabletop is a distance 2h above the floor. Block A is then released from rest at a...
Homework Statement
A 2 kg tetherball swings around a vertical pole attached to two ropes each at a 30 degree angle from vertical. Each supporting rope is 1.5 meters long, and the ball travels at 8 m/s long.
Homework Equations
The question doesn't ask what they're looking for, so I assume they...
See attached photo please.
So, I don't get how equations of motion derived. Why is it that x dot is partial derivative of H in term of p but p dot is negative partial derivative of H in term of x.
Hi There!,
I'm here just to know an answer to a question that is bothering me for a while now. We know that motion of a body under the influence of central force with given center [say A] is planar . I was thinking whether this is possible even when body is allowed to move under the influence of...
Greetings all,
I apologize for joining your forum just to inquire about something that should be relatively simple, but you seem like a group of physics geeks able to articulate coherent arguments, and I need someone/s to help me see a different perspective on how to make an argument. For the...
Homework Statement
An object with mass m = 2 kg is moving in a uniform circular motion with radius r = 2m as shown in the figure. It takes π seconds for the object to travel from θ =0 to θ = 180 degrees. What is the distance traveled by the object in 20 s...
Assume an object accelerating at a certain value dV/dt. If this object was traveling in a circular motion the centripetal force would increase as the object moves faster.
To maintain centripetal acceleration constant while the object is accelerating (in its forward motion dV/dt) I think it...
Homework Statement
An arrow is shot at 45 degrees into the sky off of a 51.2m cliff. It lands at a 35 degree angle
Homework EquationsThe Attempt at a Solution
I attempted to solve it using tangent of 35 is equal to the height (51.2m) divided by the distance it traveled which equals 72. I more...
Homework Statement
Two cars are 1.4 km apart and driving towards each other. One car starts from rest and accelerates uniformly at 1.2 m/s^2. The other car is driving at a constant speed of 18 m/s. When will the cars meet?
Homework Equations
d=vt
d=ut + 1/2at^2
d=vt-1/2at^2
v^2 = u^2 + 2ad...
Homework Statement
A bus of weight Fg is moving at a constant speed over a hill and then over a dip that has the same radius of curvature, when the bus passes over the crest of the hill, the road exerts a normal force on the bus equal to 3/4 Fg. What is the normal force the road exerts on the...
1. The problem statement, all variables, and given/known data
A block of mass m1 = 2.00kg is attached to a rope of length L1 = 0.50m, which is fixed at one end to a table. The mass moves in a horizontal circle supported by a frictionless table. A second block of mass m2 = 1.25kg is attached to...
Homework Statement
The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t=0 its position and velocity components are +1.1 cm and -15 cm/s, respectively.
(a) Find the acceleration component of the needle at t=0
(b) write an equation giving the...
Homework Statement
Which of the following correctly describes the velocity vector in each case? 2. The attempt at a solution
I got it wrong at first.
My new attempt (I have a sneaking suspicion that I am missing something important):
For the first picture:
dtheta_1/dt<0 - the angle is...
Homework Statement
An airplane propeller is 2.78 m in length (from tip to tip) and has a mass of 127 kg . When the airplane's engine is first started, it applies a constant torque of 1880 N⋅m to the propeller, which starts from rest.
Part D
What is the average power output of the engine...
New to physics and attempting to get my feet wet reading "The Quantum Universe: Everything That Can Happen Does Happen" by Brian Cox and Jeff Forshaw. Looking to get some clarification on what I hope is a simple concept regarding a particle in motion.
The author introduces the use of "clocks"...
Homework Statement
a particle moves in a circle under the influence of an inverse cube law force. Show that the particle can also move with uniform radial velocity,either in or out.
Find theta as a function of r for motion with uniform radial velocity.[/B]Homework Equations
f=-2A/r^3[/B]...
Hi everyone!
Really struggling with this question here, was hoping someone could point me in the right direction?
https://puu.sh/xVitw/4c0b89c576.png
1. Homework Statement
Set origin to bottom right.
OA is y (Which using cos(60)*R you can determine to be 0.5R).
OB is x (which you can...
Homework Statement
In a homogeneous, non-magnetic, highly insulating and viscous medium, a moving particle experiences a viscous drag given by the law f→=−bv→. Here b is a positive constant. A particle having charge q is projected with an unknown velocity from a point in the medium. It almost...