Rotational dynamics Definition and 274 Threads

Homework Statement [/B] A thin light string is wrapped around a solid uniform disk of mass M and radius r, mounted as shown. The loose end of the string is attached to the axle of a solid uniform disc of mass m and the same radius r which can roll without slipping down an inclined plane that...

about what axis is equation of angular momentum calculated(angular momentum = moment of inertia*angular velocity)? please help.

Homework Statement What is the tension in a pendulum? Is T=mgcos(theta) or is T=mg/(cos(theta)) ? and is the x component of tension is mgsin(theta) and this is the restoring force? Homework Equations Fnet=ma Fg=mg The Attempt at a Solution Maybe it depends on the problem given? But I am...

I'm wondering about how one would describe the dynamics of a rotating sphere. Consider this: a solid sphere of mass "m" and radius "r" is set to rotate about a tangent to its surface. If it is released from the horizontal position such that it swings like a pendulum, what would be the force...

Homework Statement I attached the stated questions. Mainly need help with question 2. See below for my answer to question 1.Homework Equations ΣT=Iα ΣF=ma moment of inertia of sphere: I=(2mR^2)/5 moment of inertia of disk: I=(mr^2)/2 v=rω V(center of mas)=V(tangential) -because of smooth...

Homework Statement As shown in the attached figure, 2 forces ##F_1=3N## and ##F_2=5N## are applied on the rod of mass ##1## kg.The separation between the points of application of the 2 forces is 0.2 m. If the rod undergoes only translational motion, find the length of the rod. Note that...

Question: Refer to https://www.physicsforums.com/threads/rolling-motion-of-plank-and-cylinders.93329/ I am able to understand all the points until the point v_roller+rω=v_plank. I have a tough time understanding this part. My attempt at the question: I think that the static friction at the top...

I am doing an analysis concerning the torque-free motion of an axisymmetric body (J1 = J2 != J3). The angular velocity is given \omega(t) = [\omega_t\ sin(\Omega t), \omega_t\ cos(\Omega t), \omega_{z0}] where \omega_t, \Omega and \omega_{z0} are constants. I would like to determine the...

A solid sphere and a hollow one of same mass and radii are rolled down a rough inclined plane. Which of the following is true? (A) solid sphere reaches bottom with greater speed. (B) solid sphere reaches the bottom with greater kinetic energy. ( I know that option A is correct.Thus I felt that...

Homework Statement I have two analog MEMS accelerometers ADXL337, ADXL377. The ADXL337 can measure acceleration upto +/- 3g (where g = gravitational acceleration) and ADXL377 can measure upto acceleration of +/- 200g. More than this much amount of acceleration, would create noise and random...

Homework Statement >Problem:<br>Find the Moment of Inertia of a circular disk of uniform density about an axis which passes through the center and makes an angle of $\dfrac{\pi}{6}$ with the plane of the disc. Homework Equations Moment of Inertia ($I$) is $$\int r^2dm$$ where $r$ is the...

Homework Statement Two particles of mass m1 = 14 kg and m2 = 24 kg are connected by a massless rod of length 1.4 m. Find the moment of inertia of this system for rotations about the following pivot points. Assume the rotation axis is perpendicular to the rod. A) center of rod B) end of m1...

Homework Statement Problem statement - [/B] Klepner and Kolenkow 6.15 : A pendulum is made of two disks each of mass M and radius R separated by a massless rod. One of the disks is pivoted through its center by a small pin. The disks hang in the same plane and their centres are a distance l...

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...

Hello Guys, I have a disk of diameter of 150mm and thickness of 10mm which is rotating at the constant speed of 100rpm. The disk is inside water which is approximately 4-5 cm below the surface. Disk is horizontal (parallel to the water surface). Disk is attached with the shaft of the motor. At...

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded...

Homework Statement A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. a. Draw free-body diagrams for the block and the cylinder. b. Calculate the tension in the string...

1. Homework Statement I am stuck on this problem involving tension, acceleration of a system, friction and a pulley. I have an idea of how to find the acceleration of the system neglecting the mass of the pulley, but it is not the solution. How does adding a frictionless pulley in the system...

Homework Statement I have been struggling, for over a month now, to find a way to measure instantaneous torque from a servo motor. Here's a servo that look similar to the one I'm using: https://www.servocity.com/html/spg805a-bm_standard_rotation.html I need to find a way to measure the torque...

Homework Statement I changed the problem, because I understood my error I forgot a force. It's the same problem with one motor. A motor drives two disks on a support. The support is turning clockwise at w1. Disks turn at w at start. The motor M gives a force F and a counterclockwise torque...

Homework Statement The vertical exercise wheel in a mouse cage is initially at rest, but can turn without friction around a horizontal axis through the center of the wheel. The wheel has a moment of inertia I=0.0004kg m2 and radius R = 0.06m An extremely smart pet mouse of mass m = 0.03 kg runs...

Hi,first time posting here, so please be gentle... I am studying a point mass doing uniform circular motion on a horizontal frictionless table with tension in a string fixed at one end as the center. Everything is clear if center of circle is treated as center of rotation 'O' for the $$\tau = I...

Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want). This link can rotate only 180 degrees, not...

If two spinning cylinders with different MoIs and angular speeds and different radii come in contact with each other at the curved surfaces, how to find out the final angular speeds given all initial parameters? There will be a friction acting at the line of contact and perpendicular to it as...

Homework Statement A cylinder and pulley turn without friction about stationary horizontal axles that pass through their centres. A light rope is wrapped around the cylinder, passes over the pulley, and has a 3.00 kg box suspended from its free end. There is no slipping between the rope and the...

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 )...

Homework Statement A space station shaped like a giant wheel has a radius 95.0 m and a moment of inertia of 5.03✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the...

Homework Statement http://imgur.com/eYoa8Ut Homework Equations Torque=rt=I(alpha) t-mg=-ma alpha = a/r The Attempt at a Solution t-mg=-ma is the equation for the hanging mass. To find how much this turns the small wheel, rt=I(alpha) I and r are known rt=Ia/r I'm not sure what to do from...

Homework Statement A wheel is spinning at n=1200rpm. The wheel starts to linearly decelerate, and after t=100s it stops. Determine the velocity, and acceleration of a point 10cm from the center of the mass, after 50 seconds of decelerating. The radius of the wheel is 30cm.Homework Equations...

Homework Statement A small body A is fixed to the inside of a thin rigid hoop of radius R and mass equal to that of the body A. The hoop rolls without slipping over a horizontal plane; at the moments when the body A gets into the lower position, the center of the hoop moves with velocity v0...

Homework Statement A cylinder of mass M and radius R, with moment of inertia: I_c = \frac{1}{2}MR^2 rolls down without slipping through an inclined plane with an angle of θ, while pulling a block of mass Mb with an attached frame (of insignificant mass) which is connected to the axis of...

Homework Statement Two blocks of masses m1 = 8.00 kg and m2 = 12.00 kg are connected by a string of insignificant mass. The string lies on a cylinder of mass 0.50 kg and a radius of 0.15 m. The coefficient of kinetic friction between m1 and the surface of an inclined plane is 0.10. The angle...

Homework Statement A light string is wrapped around a solid cylinder and a 300g mass hangs from the free end of the string. when released, the mass falls a distance of 54cm in 3.0s. a) Calculate the tension in the string. b) Calculate the mass of the cylinder. Homework Equations...

If I have say a stationary rod, and a particle collides with the rod whilst moving at speed v at the top end, why does the rod then proceed to rotate about the centre of mass of the system (whether that be in an elastic or completely inelastic collision where they both stick together). I...

PDF: http://www.aapt.org/physicsteam/2014/upload/exam1-2014-2-2-answers.pdf Homework Statement A disk of moment of inertia I, mass M, and radius R has a cord wrapped around it tightly as shown in the diagram. The disk is free to slide on its side as shown in the top down view. A constant...

Homework Statement a) A 1.5 kg frog sits at rest on top of a solid disk. The disk's mass is 4 kg, its radius is 1.25 m, and it rotates on a frictionless axle. The frog jumps from the disk at 3.7 m/s at an angle of 50°. Find the angular momentum of the frog about the axle as it leaves the disk...

Homework Statement A hard drive consists of a rigid circular platter (or disk) of radius 0.05 m and thickness 0.002 m. In normal operating conditions, the hard drive spins at 7200 rotations per minute. The read/write head is a light metallic element that floats just above the platter and both...

Homework Statement Answer: C Note: Sorry admins for the picture, needed to include the diagram though. Homework Equations ∑\tau = I\alpha ∑F = ma a = \alphar The Attempt at a Solution The torques must be balanced (is this reasoning already wrong?), thus, F*R1 = F_T*R2 F_T =...

Homework Statement A 0.70-kg disk with a rotational inertia given by MR^2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip, then as the mass falls and the...

Homework Statement A 8.0-cm radius disk with a rotational inertia of 0.12 kg*m^2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by a using a crank to apply a 9.0-N*m torque to the disk. The...

Hey PF! Homework Statement I've attached the problem to this post along with my free body diagram. Homework Equations Moment of inertia of a cylinder: 1/2MR^2The Attempt at a Solution Since the cylinder is moving at a constant velocity and is not slipping, ƩF = 0. For the torques around the...

Homework Statement A large wheel has a radius of 7.1 m. A rope is wrapped around the edge of the wheel and a 7.6 kg box hangs from the rope. A smaller disk of radius 1.38 m is attached to the wheel. A rope is wrapped around the edge of the disk as shown. An axis of rotation passes through the...

Homework Statement A light rigid cylinder of radius 2a is able to rotate freely about its axis, which is horizontal. A particle of mass m is fixed to the cylinder at a distance a from the axis and is initially at rest at its lowest point. A light string is wound on the cylinder, and a steady...

When I am browsing through my rotational dynamics chapter, I raise myself a question on the direction of frictional force under all kinds of possible circumstances: [FONT="Arial Black"]1. Pure rolling For pure rolling, the frictional force will always be 0; [FONT="Arial Black"]2...

Homework Statement Two disks are spinning freely about axes that run through their respective centres (see figure below). The larger disk (R1 = 1.42 m) has a moment of inertia of 1070 kg · m2 and an angular speed of 4.2 rad/s. The smaller disk (R2 = 0.60 m) has a moment of inertia of...

Torque, in particular, is always a concept that has confused me. Can the rules related to torque be derived or are they natural tendencies? (For lack of a better way to phrase this). For example, if I were trying to solve the problem of a ladder leaning against a frictionless wall, where I...

Homework Statement An oxygen molecule consists of two oxygen atoms whose total mass is 5.3x10^-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.9 x 10^-46 kg*m^2. From this data, estimate the effective distance between...

Homework Statement Given a rod of length 'l' placed upright on a smooth floor.A slight disturbance causes it to fall.Now required is the velocity with which the COM falls down when the rod makes angle θ with horizontal. The Attempt at a Solution now let the middle portion of the rod be...

A mine cage of mass 4 tonne is to be raised with an acceleration of 1.5m/s^2 using a hoist drum of 1.5m diameter. The drum’s mass is 750kg and its radius of gyration is 600mm.The effect of bearing friction is equivalent to a torque of 3kNm at the hoist drum. What isthe driving torque required...