Dynamics Definition and 1000 Threads

Homework Statement A hollow cylinder of internal radius r and external radius R and mass M is connected by a string to a weight m. What are the angular and linear acceleration of the cylinder? Assume that the cylinder is rolling without slipping. What is the acceleration of the weight and...

Homework Statement A child is tobogganing down a hillside. The child and the toboggan together have a mass of 50.0kg. The slope is at an angle of 30.0° to the horizontal. Assume that the positive y-direction is pointing in the direction of the normal force. Assume that the positive...

Homework Statement The pendulum of a grandfather clock consists of a thin rod of length L (and negligible mass) attached at its upper end to a fixed point, and attached at its lower end to a point on the edge of a uniform disk of radius R, mass M, and negligible thickness. The disk is free...

in an undergrad introductory dynamics class, my professor used tensors, and assumed things went to zero to derive equations for angular acceleration. he then proceeded to show how a rotating body with certain moments of inertia will experience unstable rotation about certain axes due to the...

Homework Statement The 30-kg reel is mounted on the 20-kg cart. If the cable wrapped around the inner hub of the reel, with radius 150mm, is subjected to a force of P=50 N, determine the velocity of the cart and the angular velocity of the reel when t=4 sec . The radius of gyration of the reel...

Suppose I have a cylinder on a fulcrum that is filled half way with a fluid, how would I model the waves in the cylinder if it were put in motion?

Hi all, With reference to the attached diagram 1, what affect will friction have on the acceleration? Below is my solution, but is there something that I can include? and is it explained correctly?: "Since friction acts as a force which opposes in this case the sliding motion of the...

Is there any kind of celestial event that could occur that could completely lock the Earth's rotation such that it is constantly facing the sun, in the same way the moon is tidally locked to the earth? What would it take? Could it be caused by the passage or entrance of a new gravitational...

Homework Statement A uniform rod of mass m and length l is pivoted at point O. The rod is initially in vertical position and touching a block of mass M which is at rest on a horizontal surface. The rod is given a slight jerk and it starts rotating about point O. This causes the block to...

Strogatz's Nonlinear and Dynamics book states that $$ \langle\sin^{2n}\rangle = \frac{1\cdot 3\cdot 5\cdots (2n-1)}{2\cdot 4\cdot 6\cdots 2n} $$ for $n\geq 1$. However, $\langle\sin^6\rangle = \frac{5}{16}\neq\frac{15}{48}$. What is the deal here?

Homework Statement Suppose that a blast wave, which might have been initiated by an atomic bomb explosion, is traveling through air at standard atmospheric conditions with a speed of 60,000 m/s find change in ( pressure , temperature , stagnation pressure , velocity ) produced by the wave...

So there's this new course at my school called "Intermediate Dynamics" and I'm wondering if there are any differences between this course and another called "Intermediate Mechanics." Dynamics is in the MAE department and Mechanics in the Physics department. Here are the descriptions...

Homework Statement water in main pipe at the street level is at a gauge pressure of 170 KPa and is moving with neglibible speed. A pipe connected to the main pipe is used to deliver the water to kitchen located on the third floor of a building, at a 15-m height from the street level. what is...

Homework Statement I just saw the equation R'=RΩ (where ' is dot, or the derivative) in my notes (unorganized obviously), and can't remember what it stands for (rotation matrices?). Can somebody please tell me what this equations means thanks. I know R is some position vector and Ω is the...

I am right now studying Rigid Body dynamics.. I have some doubts regarding Dynamics... 1) When a body is rotating as well as translating...we say that every particle of the ..lets say ROD is moving with a resultant velocity = Vcm ( translational velocity of COM) + ω.R (where R is the...

Show that all vector fields on the line are gradient systems. This is exercise 7.2.4 in the book "Nonlinear Dynamics and Chaos" by Steven H.Strogatz Thanks very much!

Hi friend I am really getting big problem in solving this question which is related to Rotational dynamics. Please help me in solving this. I will be heartily thankful to u all guys. The question is as follows ...

Homework Statement I just saw the equation R=R'Ω (where ' is dot, or the derivative) in my notes (unorganized obviously), and can't remember what it stands for (rotation matrices?). Can somebody please tell me what this equations means thanks. I know R is some position vector and Ω is the...

Homework Statement A small car with mass .800 kg travels at a constant speed of 12m/s on the inside of a track that is a vertical circle with radius 5.0m. If the normal force exerted by the track on the car when it is at the top of the track is 6.00N, what is the normal force at the bottom of...

Hi all. Reading on several books and papers, I found that the motion of a wheel moving on a flat surface are given by (assume that positive torques are counter-clockwise and the positive direction of the motion is toward the right direction): m \dot v=F J \dot ω=-rF+T for T<0, where m...

Hi, I'm new to the forum, starting off with some rotational stuff that I am not grasping well... I have diagrams for each question too, which i feel are vital to understanding the questions Homework Statement A spherical ball bearing 0.025m in diameter, rolls without slipping down an...

i was reading about derivation of Euler's equations for rotational dynamics (john taylor, classical mechanics, chapter 10) when i got stuck on one of the reasonings essentially it refers to the moment of inertia tensor, since the tensor itself about a point is dependent on the position of the...

Homework Statement A plank with a mass M = 6.10 kg rides on top of two identical, solid, cylindrical rollers that have R = 4.10 cm and m = 2.00 kg. The plank is pulled by a constant horizontal force F of magnitude 4.80 N applied to the end of the plank and perpendicular to the axes of the...

Homework Statement I've been trying to attempt this problem for the past day but I don't understand how to answer the questions. It's frustrating. If someone could point me in the right direction that would be nice. My TA did the problem in class but I still don't quite understand it. This is...

I'm getting desperate. The professor has assigned a project and has not clearly explained how to derive the answers. I'm doing the best I can but his TA's and recommended tutors for the class are always incapable of reproducing the answers either. It's a junior level dynamics class, but he's...

Hi all, Am reading a few papers for a Uni case study about structures in Turbulent Boundary Layers over a Flat Plate (water), particularly low-speed streaks. I'm confused over what mechanism causes the span wise variations in velocity that seems to cause low speed streaks. Would...

Homework Statement You are driving home from the cottage and pulling a trailer behind your car. There is a steep hill with a 12 degree incline that you must drive up. You read the instructions for the trailer hitch which keeps the trailer attached to your car. The hitch can withstand...

Homework Statement Given: m = 17kg Vi = 0 Fa=42N θ=25 Mu=0.15 T=125s Diagram: http://s14.postimage.org/euy3whikh/New_Bitmap_Image.png Find: Δd a block accellerates from rest for 125s find the displacement. Frictional forces act on the block. A force applied is 25 degrees above the...

Homework Statement An environmentally-sensitive daredevil wants to use a large mass, a rope, and a pulley to accelerate toward ramp while his motorcycle is in neutral, as shown below. If friction is negligible, what will the acceleration of the motorcycle be and the tension of the rope...

Homework Statement Steady, laminar flow of an incompressible Newtonian fluid with constant physical properties. The area of interest in the problem is in the entrance region between two wise, horizontal parallel plates separated by distance 2B. z is in the direction of flow and x is the...

Homework Statement A man drags a 71.5-kg crate across the floor at a constant velocity by pulling on a strap attached to the bottom of the crate. The crate is tilted 22.5° above the horizontal, and the strap is inclined 64.0° above the horizontal. The center of gravity of the crate coincides...

I've got the following exercise, which I've done 3 times already and I think I haven't made any mistake: A body is slid upwards through an inclined plane of angle \theta=15\degree. Determine the friction coefficient of the body with the surface of the plane if the time it takes to go upwards t_a...

I would like to pipe a water well ( using gravity alone) with a 250m run and an overall fall of 3m. A large barrier (a hill) is middle ways . The last 100m down the hill has most ,if not all the fall. The question is if I pipe this last 100m with a larger diameter (from 3/4" going to 1") would...

Is it usual to customise experiments in fluid dynamics and to what extent? I understand that lasers and imaging tools will be fairly untouchable by a fluid dynamicist, although does an experimental role require any 'tampering/customising of general system equipment i.e. rewiring/handy work...

A point of mass m, affected by gravity, is obliged to be in a vertical plan on a parabola with equation z = a.r^2 a is a constant and r is the distance between the point of mass m and the OZ vertical axis. Write the Lagrange equations in the cases that the plan of the parabola is : a) is...

Homework Statement The static friction coefficient between the grippers and the ball is 0.5, and the grippers hold the ball such that they touch the middle of the ball on opposite sides. Find the clamping force required to keep the ball from slipping out, if the ball weighs 10 lb...

Homework Statement A 5000kg rocket is launched at 44.7º with a thrust of 140,700N. a. Find an equation y(x) that describes the rocket's trajectory. b. Shape of trajectory? c. At what elevation does the rocket reach the speed of sound, 330m/s? Homework Equations F=ma The distance...

Solving a problem about a pulley system (dynamics) A 100 kg crate is supported by a rope which passes over a 25 kg pulley. A 2nd rope connects the pulley to the ceiling. The system is stationary. ƩFx=0 ƩFy=0 I am having problems setting up the free body diagram to start the problem!

Hello, I have a general question regarding what is the best controller (PI, PD, etc.) to control the position of a mobile robot in order to follow a known path. The mobile robot at hand is a mechanism (a 4 bar linkage with its two base gliding on two parallel but not straight rails) and I...

I am studying plasma physics. While treating the plasma as a fluid, we replace the generla time derivative of velocity of any particle by the convective derivative. I would like to know the reason and also what is the frame of reference when we work with fluid dynamics.

Homework Statement a 200-g projectile is fired with a velocity of 900m/s towards the center of the 15-kg wooden block, which rests on a rough surface. If the projectile penetrates and emerges from the block with a velocity of 300m/s, determine the velocity of the block just after the...

Homework Statement A 45 kg boy stands on 30 kg platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the boy. The masses of the rope and pulley are negligible. Ignore the friction in the pulley. a) If the rope and the...

Homework Statement Consider the interaction of two species of animals in a habitat. We are told that the change of the populations and can be modeled by the equations \frac{dx}{dt}= 0.1x-0.8y \frac{dy}{dt}=-0.2x+0.7y Find the solution to the above equations with initial values x(0)=9 and...

If room A is connected to the outside with a window and room A has a fan on; Would the air would try to move out from room A to the outside because there is a higher pressure inside the room? in concept

I need a lot of help with Kinematics and Dynamics so forces and motion would be what you can call that. I have a teacher that does not teach, I have had her for two years in a row now so if I had some knowledge from grade 11, It would still help me but I learned close to nothing in Grade 11 and...

Hey, I'm having problems with this questions Sally’s car is stuck in a snow bank, but she is very knowledgeable about physics. She ties a rope from her car to a tree 25.0 m away and then pulls sideways on the rope at the midpoint. If Sydney applies a force of 425 N and draws the rope over a...

I used to watch youtube videos for general physics and statics but I can't seem to find good help sources for dynamics. Does anybody know of a good youtube channel that has helpful videos for the dynamics course or any other websites that help make more sense of the class? If not, can...

Hey! I'm having some problems with this question: An electric winch is used to raise a 40-kg package and a 10-kg package vertically up the side of a building as pictured in the diagram. The magnitude of the frictional force acting between the wall and the 40-kg package is 60N. The angle the...

One question about this excercise. Why "W" isn't included in the sum of forces? Is doing work because is in the same direction of the movement, so I would assume that both the force of spring and weight would be in in my sum of forces. But this is not the case here, why is that?

Are fundamental discoveries made in fluid dynamics currently, or is it just particular solutions based upon known fundamentals? From reviewing journal literature, it appears that either application based problems have been studied (engineering), or fluids under certain conditions that form a...