Perpendicular Definition and 512 Threads

Homework Statement A 15-cm-diameter CD has a mass of 21 g . What is the CD's moment of inertia for rotation about a perpendicular axis through its center?Homework Equations I = (1/2)MR^2 3. The Attempt at a Solution I = (1/2)(0.21g).((15/2)^2) = 5.9*10^-4 kg*m^2 cant see what I am...

I know that when two lines are perpendicular their gradients multiply to -1 but I don't get the wording here. Any suggestions?

Find the equation of the line through (-9, 2); perpendicular to y= -1. Use standard form : y=mx+b

Hi, i get the math that is involved but if I have only the x,y coordinates for 2 points to connect and if i want to know what will be the perpendicular line to the line connecting these two points, how can I do that?

I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis. When I find their Components trigonometrically, I get 70N each; as Fx = 100xCos(45) = 70N Fy = 100xSin(45) = 70N Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N. Why is there discrepancy or where am I...

Let's say that we have two guys, each weighs 50 kg. They are pulling a piece of against each other as hard as they can. The tension of the rope will therefore be the force of friction acting on each of them (the same magnitude). Now, let's say that a third person joins the party and grabs the...

I have some understanding, but I'm not sure about how accurate it is: Electrostatic force is given by F = qE, where F and E are both vector quantities. If the dot product of either side and the displacement vector Δs along an equipotential line is taken, the equation becomes F⋅Δs = qE⋅Δs. F...

I have a question. If you're given a force of 20 N and its 60 degrees to the horizontal, how could you find two perpendicular forces?

The question that I'm trying to answer states "Make a vector equation of a plane that is perpendicular to the z axis." How do i ensure its perpendicular? How do i start this equation? Another question similar to this that i am also struggling states "What is the vector equation of a 2D line...

Homework Statement [/B] Consider the line whose shortest distance to the origin is 5 and that is perpendicular to the ray ##\theta= \frac {5*\pi}{7}## for r>0 Find its polar equation ##r=r(\theta)## and ##\theta_1<\theta_2## in the interval ##[0, 2\pi]## such that ##r(\theta)\geq 0## for all...

Homework Statement Describe how the dot product can be used to determine whether two vectors are perpendicular. Create a question with vectors in 3-space to illustrate this property. Solve the question as well. Homework EquationsThe Attempt at a Solution Did I do this right? I did something...

My question is perhaps as much about the philosophy of math as it is about the specific tools of math: is perpendicularity and rotation integral and fundamental to the concept of multiplication - in all number spaces? As I understand it, the product of complex numbers x = (a, ib) and y = (c...

Homework Statement Two particles A and B each carry a charge Q and are separated by a fixed distance D. A particle c with charge q and mass m is kept at the midpoint of A and B. If C is displaced perpendicular to AB by a distance x where x<<<D, find the time period of the oscillation of the...

$\textsf{Find the vector perpendicular to the plane PQR determined by the points}$ \begin{align*}\displaystyle &P(2,1,3), \, Q(1,1,2), \, R(2,2,1)\\ \end{align*} $$\textbf{ solution:}$$ \begin{align*}\displaystyle \vec{PQ}&=(1-2)i+(1-1)J+(2-3)k=&-i-k\\...

Why an object will move in circular when the acceleration is perpendicular to the velocity?

An assumption in deducing the Bethe equation is that the momentum transfer is perpendicular to the direction of the particle. ALSO In Allison & Cobb (1980), just after eq. 28, they state that the first two terms of the Photoabsorption Ionization model arise from the magnetic vector potential...

The question: The line L1 has equation r = \left( \begin{array}{ccc}4 \\-1 \\0\\\end{array} \right) + t\left( \begin{array}{ccc}1 \\1 \\-1\\\end{array} \right) , and point A has coordinates (4, 8, -3). Find the coordinates of point B on L1, such that \overrightarrow{AB} is perpendicular to...

Does anyone know where I can find information about how to calculate how much extra energy is required of a spaceship to try to thrust perpendicular (or at some angle) to the orbital plane verses flying completely/only in the orbital plane when moving outwards in our solar system? If the...

i would like to know if the forces exerted by the load on pulley 1 and 2 are equal when the motor star running , or if in pulley 1 is exerted more force because the location of the load at the end of the lifting platform. The lifting platform only moves vertically, restricted by rails. What I...

I am asking this because ∇ is also considered as a vector in some cases. Considering it as a vector in this case ,too, ( ∇× E).E = (- ∂ B/∂t).E = - ∂ (B.E)/∂t =0 Since B and E could be arbitrarily dependent on t, B.E = 0 where B and E are magnetic and electric fields respectively. This...

Not only the Problem I have attached in Picture, but there are few more where I get different answer while solving by taking Moment Component and by Common Perpendicular. [NB : The problem Stated in 'Engineering Mechanics' by Ferdinand L. Singer. Process 3 is what I did, Process 1 is what is...

The tangent passes through just one point Now i can draw it such that the angle of incidence is always 0 and incident angle is always 90 Then no image will be formed. Why does this not happen??

If the normal is always 90 to the mirror can we assume that it always passes through centre of curvature? The light rays passing through the centre are reflected back in the same direction as angle of incidence is 0 and incident angle is 90 so, the normal should pass through the centre.

Homework Statement Car 1: 2200kg Initial direction: South Car 2: 1800kg Initial direction: East Cars lock together and slide 11.25M (S 22.25 E) At an acceleration that is 9.81 m (back) (it's a coincidence that this is gravity.) Homework Equations Who's fault was the collision if the speed limit...

Two smooth spheres of masses km and m collide obliquely. the sphere of mass m is brought to rest by the impact. the coefficient of restitution for the collision is 1/k (k greater or equal to 1) Prove before the impact the spheres were moving perpendicular to each other. i have worked out k=-1...

two smooth spheres of masses 2kg and 4kg collide obliquely . the 2 kg mass is brought to rest. the coefficient of restitution is 1/2 prove before the impact the spheres were moving in perpendicular directions to each other. using conservation of momentum. 4x+2y=4p+2(0) where x...

Homework Statement Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1) Homework Equations Gradient The Attempt at a Solution I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...

Use the distance formula to find the perpendicular distance from P(1, 3) to the line y = (x/2) - 5. Any ideas on how to get started?

Homework Statement A particle of mass m1 collides with a particle of mass m2 initially moving at right angles to it(see Figure 1 below). Calculate the final velocities of each particle, and the angles at which the particles leave the collision site( as measured with respect to the original...

Homework Statement So the problem is the following : we observe the stellar aberration of a star which isn't on the zenith, so that the star forms an angle theta with the ecliptic plane of the Earth. With such a position, the star will describe an ellipse instead of a circle (typical movement...

Hi there. I very much enjoy this forum and have been doing so for a while. I have a problem and I am not sure of the explanation I came with. Suppose there is a plane that is nosediving perpendicular to Earth. What will the "passengers" feel? In the first seconds the acceleration will be equal...

why force parallel to the axis of rotation do not make any torque.

Homework EquationsThe Attempt at a Solution [/B] I was of the understanding that the slope can be calculated as mgsin20 whereas the force acting straight down through the lift is mgcos20 but the answer is mg divided by cos 20??

Homework Statement find equation of plane P that is perpendicular to line L which passes through the point (-2,-2,3) Homework Equations ... The Attempt at a Solution [/B]line L passes through the points (1,2,1) and (0,0,-3) I have worked out the parametric equations of line L to be x=1-t...

Hello to everyone, merry christmas and happy new year! I was trying some exercises on the Feynman Lectures, on the topic of statics, and I came across with a problem which, simplified until where I am stuck, asks for the tension of a cable perpendicular to a bar with a weight on the top of it...

Picture water flowing in a duct. In these kinds of scenarios, the loading exerted by the moving fluid to the solid in the perpendicular direction is often taken as being equal to the pressure of the fluid at the wall. I agree that the above assumption is true for a stationary fluid. For a...

Homework Statement :[/B] A mass is moving with constant acceleration in the x-y plane. At time t = 0s the mass’s position is 2mˆı+3mjˆ, the mass’s velocity is 3 m/s ˆı −4 m / s jˆ and the mass is subject to an acceleration of 1 m/ s ^2 ˆı + 1 m/ s^ 2 i jˆ. At what time is the velocity...

Homework Statement A particle flies along in the positive +x direction. It has a constant force F applied 30º clockwise to the x-axis. It is moving at .6 c. What is the angle of acceleration? Homework Equations a = F/(mγ3) The Attempt at a Solution [/B] I'm pretty sure I know how to do...

Say i Have 1. A perfectly spherical and perfectly rigid Ball 2. A perfectly flat and perfectly rigid wall Say i throw the ball at my FLAT wall also giving the ball a linear velocity The only contact with the wall and the ball is a point... a POINT ! So, I can as well forget about the rest of...

I mean physicists when they have to create a field they draw it with the same direction of the force, (gravitational, electric for example) i know that the magnetic field acts only on moving charges and i also know that the force is a relativistic effect of lorentz contraction, but why creating...

Homework Statement ##\vec { \dot { r } } =(t+1)\vec { A } +(1-sint)\vec { B } \quad \vec { r(0) } =\vec { C } ## a. Find an equation of the tangent line to the curve at ##\vec { r(0) } =\vec { C } ##. b. Use a definite integral to find ##\vec { r(t) } ## c. If ##A## and ##B## are non...

Homework Statement ##W = x^2+5y^2## Show that ##\nabla W## is perpendicular to the level curves of W at ##(X_0, 0)## Homework Equations ##\nabla f(x,y) = <\frac {\partial f} {\partial x} , \frac {\partial f} {\partial y}>## The Attempt at a Solution I know that the gradient is always...

The no slip condition has been described as the adhesion of a fluid to a solid surface setting the relative fluid velocity to zero - cohesion (viscous stress) between fluid elements spreads evenly the velocity gradient through the boundary to the free stream. This also infers that the pressure...

Homework Statement Proof that if the slopes of two lines a1, a2 (that are not vertical), m1,m2 satisfy: m1*m2 = -1, then the lines are perpendicular. Homework EquationsThe Attempt at a Solution I tried to use the tan function, so that m1 = tanΘ where Θ1 is the angle of the line formed from x...

Homework Statement Imagine two motorcycle gang leaders racing at relativistic speeds along perpendicular paths from the local pool hall, as shown in Figure 1.21. How fast does pack leader Beta recede over Alpha’s right shoulder as seen by Alpha? Solution Figure 1.21 shows the situation as seen...

Say that I have two vectors that define a plane. How do I show that a third vector is perpendicular to this plane? Do I use the cross product somehow?

I am given the following problem: Show, using vectors, that the diagonals of an equilateral parallelogram are perpendicular. First, imagine that the sides of the equilateral parallelogram are the two vectors ##\vec{A}## and ##\vec{B}##. Since the figure is equilateral, their magnitudes must be...

Homework Statement The book ("Real World Physics") says A virtual image in a plane mirror is on the perpendicular from the object to the mirror Homework Equations I know that the normal line is perpendicular to the surface of the mirror And I know that the angle of the incidence and reflection...

Hello! I'm currently studying Projectile Motion and Motion in Two Dimensions now in Physics class, and I happened to quickly jot down what my teacher said onto my computer. I came across the note and it says "Vector forces cannot be perpendicular to each other." I'm a little unsure of what is...

I am struggling with this question, it would be easy enough if the triangle was equilateral but that is not necessarily the case. Let (ha, hb, hc) be heights in the triangle ABC, and let Z be a point inside the triangle. Further to this, consider the points P, Q, R on the sides AB, BC and AC...