Rotational Definition and 1000 Threads

Problem: "Two blocks of equal masses m are attached by an ideal string. One mass lies at radial distance r from the center of a horizontal turntable rotating with constant angular speed of 6 rad/s, while the second hangs from the string inside the hollow spindle of the turntable.The coefficient...

Homework Statement a 3 kg mass is on the end of a metal rod which is pivoted at one end. the mass of the rod is 2kg its length is 4 meters Homework Equations I=(ML^2)/3 The Attempt at a Solution the rotational inertia of the rod itself is 10.6 but i don't know how the 3kg mass at the end...

Homework Statement Find the linear (or tangential) velocity of a point on the Earth's equator in the frame of reference about a stationary rotational axis as it spins over the course of one day. Homework EquationsThe Attempt at a Solution I do not understand what the frame of reference is?? If...

1. The problem A 6 kg block is released from a height of 5 m on a frictionless track and goes into a half pipe with a radius of 2 m. Determine the tangential and radial components of the acceleration when the block reaches a height of 2 m.Homework Equations Ac= v^2/r. At = r*angular...

Can't Even Start Please Help And Soon Exam Tommorow.

Homework Statement Please see attached picture. Homework Equations Shown in picture The Attempt at a Solution It's a textbook example that has a solution. At the middle right hand side of the picture, they say "From Eq... Vcm = Rw" (Where 'cm' is centre of mass) I don't understand why this is...

Homework Statement A spring of stiffness k is attached to a wall and to the axle of a wheel of mass m, radius R, and moment of inertia I = βmR^2 about its frictionless axle. The spring is stretched a distance A and the wheel is released from rest. Assume the wheel rolls without slipping. At...

I'm having difficulties understanding how I should calculate the angular velocities of a rigid body when the inertia tensor is given in body coordinates and has off diagonal elements. Let's assume I have an inertia tensor ## I = \begin{bmatrix} I_{xx} & -I_{xy} & -I_{xz} \\ -I_{yx} &...

A 61 cm diameter wheel accelerated uniformly about its center from 120 rpm to 280 rpm in 4.0 seconds. Determine the Angular acceleration So I converted the 120 and 280 rev per min to radians per s with 45238.93 rad/s and 105557.51 rad/s and used them as angular velocity final and initial. then...

I'm planning on carrying out an investigation with a golf ball and projectiles. Is there any type of equipment/sensor that I can used to measure the rotational speed/angular velocity? I know a gun chronograph can be used to detect the velocity but what can I used to detect the angular velocity...

Homework Statement Suppose that some time in the future we decide to tap the moon's rotational energy for use on earth. In additional to the astronomical data in Appendix F in the textbook, you may need to know that the moon spins on its axis once every 27.3 days. Assume that the moon is...

Homework Statement The Sun rotates on its axis every 25 days. The sun currently has a radius of 7X10^8 m. When it expands into a Red Giant (in about 4 billion years) it will have a radius of 1.5X10^11 m. What will its rotational period be assuming the same mass for both, and they are both...

I tried to use this formula: KE=(1/2)(I)(w)^2, and work=change in KEFor the first question, i tried to plug the number into the rotation kinetic energy formula: 3600rpm=376.8rad/s (0.5)(2,000kg)(0.125m)^2(376.8rad/s)^2 I found out this was the answer 1.1 x 106 J, but I got 2218410J For the...

I have a moving body with constant linear and rotational acceleration. Given a starting condition (position, orientation, linear and angular velocities), how can I combine the equations of motion to give a position and orientation a given time on?

Homework Statement Consider a uniform rod of mass 12 kg and length l.0 m. At its end, the rod is attached to a fixed, friction-free pivot. Initially the rod is balanced vertically above the pivot and begins to fall (from rest) as shown in the diagram. Determine, a. the angular acceleration of...

Homework Statement http://postimg.org/image/9fw7awqov/ The question is to write the Laplace transformed equations of motion for the system Homework EquationsThe Attempt at a Solution I am confused about a couple of things: why is an angle is not defined for the rotation of J2. Does it means J2...

Homework Statement A 2kg , 0.2 m diameter turntable rotates at 100 rpm on frictionless bearings. Two 0.5 kg block fall from above, hit the turntable simultaneously at opposite ends of the diameter, and stick. What is the turntable's angular velocity (in rpm) just after? Homework Equations L= I...

Homework Statement A cart whose body has mass M = 1.5 kg is set on four tires each of which has mass m = 0.3 kg and radius r = 0.1 meters. Each tire can be treated as a solid disk with rotational inertia mr2/2. The cart is set on an incline a height h = 1.2 meters high and released. At the...

Hello, I am currently attempting to cover rotational motion using Halliday's Fundamentals of Physics. I understand very well the concept of moment of inertia as defined as the sum Σmi*ri2. However, the textbook argues that if there are too many particles, the moment of inertia can be defined as...

Homework Statement A small ball with mass M attached to a uniform rod of mass m and length l pivoted at point o and attached to two springs with spring constant k1 and k2 at distance d1 and d2 from point o as shown in Fig 2. The system oscillates around the horizontal line. Assume the system...

Homework Statement Hi there, I have a question that I'm not sure how to go about solving: I've been given a series of transitions in the microwave spectrum of 31P14N and have assigned these Jinitial and Jfinal quantum numbers, calculated the bond length etc. The next part says that when 31P14N...

Hey Guys, Can you tell me how to solve this one, Need not give me direct answers but just take a look at this : Consider two disks A and B of equal radius, let m1 be the mass of disk A and m2 be the mass of disk B, Both are moving towards each other with Velocity v1 and v2 respectively, If they...

When you put o disc on top of a plank and if you pull the plank, the disc rotates but stays stationary. Here the friction between the plank and disk produces an unbalanced torque and hence it spins.But this friction should also cause an acceleration in the disc right? Then why does it remain...

Homework Statement In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away...

What I want to do is model the rotational behaviour of two bodies (1 and 2). They are connected by three virtual rotational springs (representing a link between them). For a normal (translational) spring the forces on body 1 in X, Y, and Z would be easily calculated as: $$ \mathbf{F}_1 =...

Homework Statement A frictionless pulley has the shape of a uniform solid disk of mass 5.00 kg and radius 28.0 cm . A 1.40 kg stone is attached to a very light wire that is wrapped around the rim of the pulley, and the stone is released from rest. As it falls down, the wire unwinds without...

Homework Statement The lightweight pivoted bar in the figure will be in rotational equilibrium when a 200N force acts (a) down at D (b) up at B (c) down at E or up at C (d) up at C only (e) none of these Homework Equations Torque = Force x Distance ∑Torque= 0 for rotational equilibriumThe...

Homework Statement A wheel of radius R starts from rest and accelerates with a constant angular acceleration α about a fixed axis. At what time t will the centripetal and tangential acceleration of a point on the rim have the same magnitude? Homework Equations acp=r x ω2 at= r x α ω= 2π / T...

Homework Statement [/B] A particle of mass m slides (both sideways and radially) on a smooth frictionless horizontal table. It is attached to a cord that is being pulled downwards at a prescribed constant speed v by a force T (T may be varying) Use F=ma in polar coordinates to derive an...

Hey! I have a problem. The problem is simple: calculate CO2 rotational constant. I have values for J (ground state and excited state), with those grades I have to calculate rotational constant. I know that for J=0,2,4.. it is just in ground state and for J=1,3,5..it is excited state. But how do...

Homework Statement You have been assigned the task of designing a flywheel capable of storing the translational kinetic energy of a 600 kg car traveling at 100 km/hr. The flywheel is to be manufactured out of steel and the maximum rotational speed is 12,000 rpm. a. Assuming that the flywheel is...

I'm working on a project now and I'd like to know which type of airflow would power a turbine faster/better straight or rotational? Or will rotational airflow even have any effect on the turbine...? P.S. When I say rotational airflow, I mean circular airflow that rotates in the same direction...

1. Homework Statement A solid sphere (mass of m, radius of r and I=2/5 mr2) is rolling without slipping on a rough surface with a speed of v. A ramp (mass of 2m and angle of θ) rests on a smooth surface and is free to slide on the surface. As the ball rolls up the ramp, the ramp begins to move...

Homework Statement [/B] A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed W0. It is then lowered, and at the instant its edge touches the ground the speed of the axle (and CM) is zero. Initially the wheel slips when it...

Homework Statement A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), it's velocity with respect to the road is Homework Equations v=ω×rThe Attempt at a Solution Well the...

Homework Statement A seesaw with a mass of 5 kg has one block of mass 10 kg two meters to the left of the fulcrum and another block 0.5 m to the right of the fulcrum. If the seesaw is in equilibrium, A. find the mass of the second block. B. find the force exerted by the fulcrum I have trouble...

I'm beginning the chapter of Rotational Motion and Angular Momentum and it says the following which got me confused: Source: http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@8.32:68/College_Physics When I was introduced acceleration at the beginning, it was stated that an...

Homework Statement Cylindrical shape pulley ( m = 6 kg, R = 0.18 m) is rotating at a frequency f = 10 s-1. Due to constant torque it stops. Calculate the work done by the breaking force. Homework Equations w = 2πf The Attempt at a Solution [/B] I can calculate the angular velocity: w = 2πf =...

Homework Statement Same mass sphere and cylinder are rolling on a horizontal plane. Which part of each objects kinetic energy does objects rotational energy make up? Homework Equations Erotational = 1/2 Iw2 Ekinetic = 1/2 mv2 The Attempt at a Solution [/B] I know, that moments of inertia...

Homework Statement So a car owner wants to change his current tires and rims to a wider set of tires and rims for increased handling ability. However, the owner does not want to lose any acceleration performance due to the increased friction of having wider tires. To combat this, the owner...

Homework Statement Two discs of radius R and r are fixed to each other, i.e., they rotate together. Strings are wound around both discs and two equal masses M are connected to the ends of the strings (see Figure 1). Find the angular accelerations of the discs, the accelerations of the masses...

Homework Statement A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of 6.55 kg, a radius of R = 38.0 cm and is in the shape of a ring. A mass M = 1.85 kg is attached to the end of a string which is wrapped around an inner hub which has a radius r = 5.40...

Suppose I have some sort of rigid body, a solid sphere let's say. For simplicity's sake let's assume that the sphere can only rotate about a single arbitrary axis through the center of mass. If the center of mass of the sphere is traveling with a constant velocity (with respect to some arbitrary...

Rotational Mechanics... Hinges and Normal Reactions -- Please help Could anyone please explain me the reason for two normal reactions on a hinge attached to a door. Also if there are two hinges the direction of the horizontal component of normal reaction is opposite to the direction of the...

Homework Statement Given an axis vector u=（-1, -1, -1) , find the rotational matrix R corresponding to an angle of pi/6 using the right hand rule. Then find R(x), where x = (1,0,-1) Homework Equations I found the relevant equation on wikipedia (see attachment) The Attempt at a Solution I feel...

Homework Statement A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 6.03 rad/s. Her moment of inertia about this axis is 16.1 kg·m2. A short time later the aerialist is in the straight position, as...

Homework Statement [/B] A 0.20-kg block and a 0.25-kg block are connected to each other by a string draped over a pulley that is a solid disc of inertia 0.50 kg and radius 0.10 m. When released, the 0.25-kg block is 0.30 m off the ground. What speed does this block have when it hits the ground...

Homework Statement A child of mass m is supported on a light plank by his parents, who exert the forces F1 and F2 as indicated. Find the forces required to keep the plank in static equilibrium. Use the right end of the planks as the axis of rotation. ( Answer: F1=(1/4)mg, F2=(3/4)mg )...

In the figure A has mass 4 kg. B and C are identical uniform discs, each of mass 2 kg. The string supporting A is ideal. Obtain the acceleration of A I have just one question, Why is pulley C undergoing translational motion ?, it should be rotational motion because it rotates about a fixed axis

Homework Statement A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.) (a) What is the...