Angular velocity Definition and 841 Threads

So there's a circular helix parametrized by \vec x(t)=(a\cos(\alpha t), a\sin(\alpha t), bt) and you have the matrix K given in the Frenet-Serret formulas. In the book I'm reading it says that -\alpha^2 is the nonzero eigenvalue of K^2. Can someone explain how they know this is? I understand...

Hey everyone, I have a 3D ball that is hit with a force 'F' at a particular position on the ball 'P'. How can I approximate (for real time simulation) the angular velocity of the X,Y and Z axis? Intuitively, the further the impulse is from the centre of the ball, the faster the ball will...

First...hopefully this is in the right section and that gem of a title makes sense. :smile: We were having a discussion at work on the topic of launching satellites and ships launching missiles. First off the satellites. The comment was made that it is better to launch a space bound...

Homework Statement Hey guys, I just read Physics, by Halliday, Resnick and Krane. There's a chapter on rotational dynamics, and the example goes like this: A yo-yo of total mass M = 0.24kg consists of two disks of radius R = 2.8cm connected by a thin shaft of radius R0 = 0.25cm. A string of...

Hi All, I have a rigidbody simulation and I'm trying to calculate the local angular velocity of the object using the derivative of it's orthogonal rotation matrix. This is where I'm stuck as I haven't been able to find an example on calculating the time derivative from two matrices at t=n and...

Homework Statement A conical pendulum is formed by attaching a 0.900 kg ball to a 1.00 m long string, then allowing the mass to move in a horizontal circle of radius 20.0 cm . What is the ball's angular velocity, in rpm? Homework Equations v=\sqrt{}L*g*sin(\vartheta)*tan(\vartheta)...

Homework Statement A pulley having a rotational inertia of 1.1 10-3 kg·m2 about its axle and a radius of 23 cm is acted on by a force, applied tangentially at its rim, that varies in time as F = 0.50t + 0.30t2, where F is in Newtons and t in seconds. If the pulley was initially at rest, find...

Homework Statement This isn't a homework problem, but I'm trying to do the calculations for a catapult I built to see if its actual performance matches the theoretical performance. I'm stuck trying to map the trajectory of the projectile. Here is the picture for reference...

Circular motion...angular velocity... Homework Statement This is a general question i have...Lets say a particle is moving in a plane (in any arbitrary way may or maynot be following any equation)...Now we are told to find the angular velocity of the particle with respect to a reference point...

Angular velocity question... Homework Statement Assume that a light source always emits a single thin ray of light...Now such a light source is kept in front of a long wall. The light source rotates at a constant anticlockwise angular velocity w. Now at a certain instant the light ray is r...

So let's say i have two cubes. If one of them slams into the other (assuming it isn't moving at all) then the force vector is just going to be the direction the first cube was moving in correct? But say that this first cube also had angular velocity on some arbitrary axis, in other words it's...

Homework Statement A wheel has six spokes of length 30 cm. The wheel is rotating with an angular velocity of 2.5 rotation per second. We want to throw an arrow, of length 24 cm, through the wheel. What is the minimal velocity required for the arrow to go through the wheel without touching the...

Homework Statement Car runs at 55 mi/hr. and the nail is lodged in tire 13 in from center of wheel, then what is the angular velocity of the nail in rad/hour? Homework Equations w= v/r The Attempt at a Solution First I will convert 55 miles into inches. 55 mile * 5280 FT/mile *...

[PLAIN]http://img218.imageshack.us/img218/8969/ferriswheelmd.jpg This is giving me a lot of problems, and honestly, I'm not sure on how to get started. Any guidance is appreciated! Thanks!

Homework Statement Calculate the angular velocity of the second, minute, and hour hand of a watch. Homework Equations Assuming the watch is functioning normally, a second hand must travel the entire 360 degrees in 60 second. The formula ω= ɵ/t would be used, where ω is angular velocity...

Suppose I have a ring of mass 'M' rotating about an axis passing through its center with constant angular velocity 'w', now if its mass changes by dm due to some unknown reason during rotation, will the angular velocity change, assuming no external force acts on it during any point of time?

From "[URL Wikipedia - Earth's rotation[/URL] The angular speed of Earth's rotation in inertial space is (7.2921150 ± 0.0000001) ×10−5 radians per SI second (mean solar second).[11] Multiplying by (180°/π radians)×(86,400 seconds/mean solar day) yields 360.9856°/mean solar day, indicating...

So I've got a pedal which sweeps through pi/2 in 1 complete cycle (frequency is known). Is its angular velocity (pi/2)*f or 2pi*f just the same? (considering that it doesn't sweep through 2pi but pi/2)

Homework Statement An airplane propeller is rotating at 1900 rev/min. Compute the propellers angular velocity. Homework Equations The Attempt at a Solution I know 1rev/min= 2pi/60 rad/s so i multiplies 2pi by 1900 and got my answer to be 3800pi/60 rad/s but idk if that's correct? someone please...

Homework Statement A uniform rod of length L (2.6 m) and mass M (10.2 kg) is free to rotate on a frictionless pin through one end. The rod is released from rest in the horizontal position, at t = 0. (a) Use energy considerations to find the angular velocity of the rod when it has...

1. A cylinder, of mass 2 kg, and a radius of 1 m, starts from rest, at point A, with its axis 3.5m above a flat stretch of ground, then rolls down a 30 degree slope as shown. After rolling a few meters horizontally, it rolls up another 30 degree slope and emerges on a flat surface 2 m above the...

Homework Statement The angular position of a point on a rotating wheel is given by θ = 2.0 + 4.0t2 + 2.0t3, where θ is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 4.0 s? (d)...

A small rubber wheel (radius of 2.60 cm) is used to drive a large pottery wheel (radius of 33.00 cm), and they are mounted so that their circular edges touch. If the small wheel accelerates at the rate of 7.10 rad/s2, and there is no slipping, what is the angular acceleration of the large...

the statement: a child runs at 3m/s and jumps tangentially onto a stationary merry-go-round. the moment of inertia of the merry-go-round is 360kgm2 and the radius is 2.0m. what is the angular velocity of the child and the merry-go-round? answer- 0.500rad s-1 or 0.500s[SUP]-1[/SUP i...

Homework Statement Hi all, I am a bit confused about angular frequency, specifically in the case of a pendulum (bob pendulum or physical pendulum). Also, what's the difference between angular frequency and angular velocity? Homework Equations I understand that a physical pendulum is...

Homework Statement I did: Center of mass = m(R+r) / M+m = 0.0708*0.0956 / (0.123+0.0708) = 0.034925 m I did: sys = m1, m2 Pf = Pi + Isystem => (M+m) v = mvi => v = m*vi / (M+m) = 0.533375 m/s How to get start on this part? Please help! Please check if part a and b...

bar (length L) is turned with angular velocity ω, on a horizontal level. Αt length of the bar, there is a ball (mass m) which rolls (We suppose that there is no friction force). The ball begins from constant utmost the bar with initial velocity u0. When the ball reaches in the L? Can you help...

Homework Statement A thin, non-conducting ring of mass m, carrying a charge q, can rotate freely about the axis. At the instant t=0 the ring was at rest and no magnetic field was present. Then suddely a magnetic field B was set perpendicular to the plane. Find the angular velocity acquired by...

Homework Statement A 230 kg beam 2.7 m in length slides broadside down the ice with a speed of 18 m/s. A 65 kg man at rest grabs one end as it goes past and hangs on as both he and the beam go spinning down the ice. Assume frictionless motion. (a) How fast does the center of mass of the...

A torque of 10 N m is applied to a 10 kg disk of radius 0.2 m initially at rest. What is the angular acceleration of the disk? I used I=1/2mr^2 so 1/2*10*0.2^2=.2 10Nm/0.2= 50 rad/s^2? (With regard to the previous problem) The applied torque of 10 N m gets the disk rotating starting...

If I have a bat speed of 74mph, how do I figure out how much angular speed that has? I cannot find a conversion or an equation anywhere.

Homework Statement A rotation wheel required 3.0 s to complete 37 revolutions. its angular speed at the end of the 3.0 s interval is 98 rad/s. what was the original angular speed of the wheel? Homework Equations average omega = change in angle/change in time The Attempt at a...

Homework Statement A 500 g steel block rotates on a steel table while attached to a 2.0-m-long massless rod. Compressed air fed through the rod is ejected from a Inozzle on the back of the block, exerting a thrust force of 3.5 N. The nozzle is 70 degrees from the radial line, so that the net...

Homework Statement A disc off a mass m1 is spinning freely at omega1(w1). A second disk of the same radius but smaller mass m2=m1/4 is dropped onto the first , and it sticks. What is the angular velocity of the two disks The Attempt at a Solution I honestly have no idea

Homework Statement A student hold a 2.0 kg textbook to their chest as they spin at an angular velocity of 6 rad/sec. Assuming the mass moment of inertia of the student to be 1.4 kgm^2, what is the angular velocity if the student hold the book 0.7 meters awayHomework Equations The Attempt at a...

Homework Statement A rotor of moment of inertia IR and outer radius R spins about a vertical axis. The rotor mount is not friction free. Rather, there is a small constant friction torque of magnitude τf . A string of negligible mass is wound around the outside of the rotor. The string is...

Homework Statement A medical laboratory centrifuge is rotating at 377 rad/s (3600 rpm). When it is switched off, it rotates 78 times before it comes to rest. Assuming constant angular deceleration, what is the angular deceleration? Homework Equations w=at+w(initial) The Attempt at...

Homework Statement A solid body rotates with deceleration about a stationary axis with an angular deceleration \beta \propto \sqrt{\varpi} , where \varpi is the angular velocity. Find the mean angular velocity of the body averaged over the whole time of the rotation if at the initial moment...

Homework Statement A shell acquires the initial velocity v = 320m/s, having made n = 2.0 turns inside the barrel whose length is equal to l = 2.0m. Assuming that the shell moves inside the barrel with uniform acceleration, find the angular velocity of its axial rotation at the moment when the...

Homework Statement I'm trying to create a graph showing the relationship between radius and angular velocity for a toriod space station that maintains a constant angular acceleration of Earth's gravity (9.8 m/s^s) on it's rim. Homework Equations ac = r\omega^2 The Attempt at a Solution...

Homework Statement You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 57.0m away, making a 2.00° angle...

Alright, so I am a programmer. I am writing a physics engine for a project at school and I am having a lot of trouble understanding rotational physics. As of now, the tools I have to work with are the point of collision for an object, it's velocity, it's acceleration (gravity), and it's center...

Homework Statement A merry-go-round is a common piece of playground equipment. A 2.85 m diameter merry-go-round with a mass of 212.0 kg is spinning at 22.5 rpm. John runs tangent to the merry-go-round at 5.76 m/s, in the same direction that it is turning, and jumps onto the outer edge...

This is a statement in my book - "The relative velocity of a satellite moving in the direction of Earth's rotation (for an observer on earth) is given as Vs - Ve." We always define relative velocity of a particle say P in a frame of reference S1 accelerating w.r.t to an inertial frame of...

Homework Statement This problem is for a cordless drill. http://img718.imageshack.us/img718/8531/drill1.jpg Homework Equations [PLAIN][PLAIN]http://img442.imageshack.us/img442/3511/drill2.jpg where N denotes number of teeth w denotes angular velocity The Attempt at a...

Homework Statement A 5.10 coin is placed 16.0 from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of = 0.810 and = 0.510. What is the maximum angular velocity with which the turntable can spin without the coin sliding...

1. Homework Statement [/b] The operation of “reverse” for a three-speed automotive transmission is illustrated schematically in the figure. If the shaft is turning with an angular velocity of Wg= 30 rad/s, determine the angular velocity of the drive shaft H. Each of the gears rotates about a...

1. So this is one of my homework problems and I just can't seem to get it, and my attempts are verging on pathetic. I feel like this shouldn't be this hard, maybe I'm just missing something. This is the acceleration vs. time graph...

Homework Statement radii R₁, R₂, angular velocity ω₁, ω₂ Homework Equations Two particles 1 and 2 describe co-planar concentric circles of radii R₁ and R₂ with angular velocities ω₁ and ω₂ as shown in the figure. Find the angular velocity of A with respect to B. The Attempt at a...

Homework Statement A ring of mass m free to slide on a fixed smooth horizontal wire is attached to one end of a string of length 60cm. The other end of the string is attached to a particle of mass 2m. The ring and the particle are initially held at the same horizontal level with the string...