Rotational motion Definition and 614 Threads

Suppose there are two discs held in contact such that they rotate around the same axis of rotation. A torque is applied to one of the discs, and due to friction the other disc accelerates. Using calculus I found the torque applied due to friction for a disc to be ##\frac {2μF_N r} {3}##, meaning...

Homework Statement [/B] A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the...

Homework Statement There are two discs with equivalent density and thickness. One has radius r1 while the other has radius r2. r2 is twice as great as r1 The larger disc has an initial angular velocity ω. The two discs then come in contact with one another and friction causes them to rotate...

Homework Statement [/B] A wheel, of radius 200mm, rolls over the top of a hill with a speed of 20m/s and negligible friction losses. (I = 1/2mr^2) Homework Equations [/B] Find the speed of the wheel when it is 10m below the top. The Attempt at a Solution [/B] mgh = 1/2mv^2 + 1/2IW^2 W=...

Problem A 60kg woman walking at a speed of 1.0 m/s steps onto a long plank that has a mass of 60kg. Upon stepping on the plank, both she and the plank begin to slide with speed v and spin with angular rate ω on a frictionless surface. 1. How far from the woman is the center of mass of the woman...

Homework Statement A 500-N person stands 2.5 m from a wall against which a horizontal beam is attached. The beam is 6 m long and weighs 200N (see diagram below). A cable attached to the free end of the beam makes an angle of 45 degrees to the horizontal and is attached to the wall. Homework...

Homework Statement A 24kg metal ring with 24cm diameter rolls without slipping down a 30 degree incline from a height of 3.4 m. 1) According to the law of conservation of energy what should be the linear speed of the ring at the bottom of the ramp 2) if the ring has a moment of inertia of...

Homework Statement an object starts from rest and has a final angular velocity of 6 rad/s. the object makes 2 complete revolutions. find the object's angular acceleration. Homework Equations wf^2=wi^2+2αd The Attempt at a Solution Not sure what to do with the revolutions, would it take act as...

I am really troubling to understand the rotational motion concept.Like angular accceleration,angular velocity torque ext.I don't know, I listened my professor's video lectures, I looked some online course pdfs but I need to learn the basics and I need more basic practice for simple...

1- I am trying to understand the rotational motion and In most books there's ##\vec θ## unit vector which its, ##\vec θ=(-sinθ,cosθ)## I can see that If ##\vec r## unit vector is,##\vec r=(cosθ,sinθ)## then , ##\frac {d\vec r} {dt}=\vec θ## Like calculating ##\vec v=\frac {d\vec r}...

Homework Statement An empty ball , of mass m moment of inertia I = (2m.r²)/3, is rolling across the path shown below : there is friction fr from A to C . r is the radius of the ball , and R is the radius of the circular part within the path . what would be the minimal height h , so...

http://imgur.com/a/8QjoW http://imgur.com/a/8QjoW Hello- I am trying to determine the dynamics of this linearly-damped hinge. Assuming that: v(0) = 0 damping constant = b door has mass = m I was able to determine that: ∑Fx = -Fd * cos(45-θ/2) + Rx = m*dvx/dt ΣFy = -Fd * sin(45-θ/2) - Fg +...

Homework Statement In bicycling, each foot pushes on the pedal for half a rotation of the pedal shaft; that foot then rests and the other foot takes over. During each half-cycle, the torque resulting from the force of the active foot is given approximately by τ = τ0 sin ωt, where τ0 is the...

Homework Statement : A uniform rod of weight W is free to rotate about a hinge at one end. The hinge is fixed to a wall. If the rod is released from a horizontal position, what force will it exert on the hinge just after being released? a)W b)W/2 c)W/3 d)W/4 choose the correct option[/B]2.The...

A flying object is moving in 3D space having translational velocity and the object is also rotating. Consider a body frame (xb-yb-zb) attached to the C.G of the moving body. Hence the body attached frame is also translating and rotating (as the object is flying) with respect to a fixed inertial...

Homework Statement A solid spherical ball of mass 0.75 kg and radius 5.0 cm is thrown onto a horizontal surface with coefficient of kinetic friction μ . It’s initial velocity at time t = 0 is horizontal and its initial angular velocity is zero. After rolling with slipping for a time t1 = 0.76...

Homework Statement A spherical ball of mass “m”, moment of inertia “I” about any axis through its center, and radius “a”, rolls without slipping and without dissipation on a horizontal turntable (of radius “r”) describe the balls motion in terms of (x,y) for a function of time. **The...

Homework Statement So I need to move this rod with length r from point A to B as shown. It has to rotate from A to B which is 90° within 10 seconds. What I want to calculate is the torque and power required if a motor was to produce this motion (location of the motor is shown in the diagram)...

1. 2. Well, these are two pics on circular motion, i found on net... If the objects had a zero rotational motion before circular motion, and the next moment suddenly a force acts ( perpendicular to their linear momentum ) such that they move in circular motion,... which of these pictures...

Homework Statement I have an angular acceleration and torque graph. I know it should be a straight line between the points, but my question is, if you extend the line toward the angular acceleration, why it doesn't go to the zero point? It is about 0,6. Homework EquationsThe Attempt at a...

Homework Statement I'm doing a question from a past paper, preparing for an upcoming exam. There is no solutions so I was wondering if my answer is correct for all parts. Take a star to be a uniform sphere with mass M_{i}=3.0 \times 10^{30} Kg and radius R_{i} = 7.0 \times 10^{8}m that...

Homework Statement A uniform thin rod of Length L and mass M is pivoted at one end is held horizontally and then released from rest. Assuming the pivot to be frictionless, find a) Angular velocity of the rod when it reaches its vertical position b) The force exerted by the pivot at this time...

Homework Statement this is a question just to help with my understanding: ... when Torque (kg m^2/s^2) and the Moment of Inertia (kg m^2) are known and used to find angular acceleration, ... T(net)/I, are the units for the resulting acceleration rad/s^2 Thanks :-) Homework Equations...

I know that to calculate the torque about an axis, we can choose any point on that axis and find the torque about that point and take the component along the direction of the axis.Buy what is the proof behind this theorem?

Homework Statement A child is at a playground, and chooses to try the spinning disc (see figure). The radius of the disc is 2.00 m, and the coefficient of static friction between child-surface and disc-surface is μs = 0.350. In the following questions, you must provide algebraic equations as...

Hi I have been dealing with a fluid mechanics pressure gradient problem and from a statistical view point I can see how it resolves itself but am puzzled as to how it can occur at the molecular scale from a conservation of linear momentum perspective if Momentum is a conserved quantity While...

Homework Statement Homework Equations Centripetal acceleration$$=\omega ^2R$$ Coriolis acceleration $$=2v_{rot}\omega $$ The Attempt at a Solution [/B] Think of the mass as lying on an incline. The forces I know are parallel to the incline are $$mgsin(\alpha), \mu N$$ Forces I know are...

Homework Statement A 500.0-g bird is flying horizontally at 2.25 m>s, not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 cm below the top(Fig. P10.85). The bar is uniform, 0.750 m long, has a mass of 1.50 kg, and is hinged at its base. The...

Homework Statement Two metal disks, one with radius R1 = 2.50 cm and mass M1 = 0.80 kg and the other with radius R2 = 5.00 cm and mass M2 = 1.60 kg, are welded together and mounted on a frictionless axis through their common center, as in Problem 9.77. (a) A light string is wrapped around the...

Hello Gurus, What are the forces opposing rotary motion? And how to calculate them? For eg., if we have a shaft rotating about it's own axis, are there any other forces that oppose this motion other than bearing friction, like air resistance or some other forces. And how to calculate these...

Homework Statement A 0.23-kg turntable of radius 0.31 m spins about a vertical axis through its center. A constant rotational acceleration causes the turntable to accelerate from 0 to 26 revolutions per second in8.0 s. Calculate the torque required to cause this acceleration. Homework...

Homework Statement The system shown in (Figure 1) consists of two balls Aand B connected by a thin rod of negligible mass. Ball Ahas three times the inertia of ball B and the distance between the two balls is ℓ. The system has a translational velocity of v in the x direction and is spinning...

Homework Statement A pendulum is made of a bob dangling from a lightweight string of length ℓ. The bob is pulled sideways so that the string makes an angle θi with respect to the vertical, then released. As it swings down, what is the rotational speed of the bob as a function of the changing...

One end of a thin, uniform rod is connected to a frictionless hinge as shown in Figure 1. The rod has a length of 0.8 mand a mass of 2 kg. It is held up in the horizontal position (θ=90∘) and then released. 1)Calculate the angular velocity of the rod at θ=90∘. 2)Calculate the angular...

RHomework Statement A What is the velocity of the mass at a time t? You can work this out geometrically with the help of the hints, or by differentiating the expression for r⃗ (t) given in the introduction. (Figure 2) Express this velocity in terms of R, ω, t, and the unit vectors i^ and...

Homework Statement A projectile of mass m is fired from ground level with speed v0 and at angle ##\theta## with respect to the horizontal. Basically there is a projectile from start to finish, with an pivot starting at the x coordinate for the highest point on the projectile. The teacher wants...

Hello everyone, I am not an engineer, so I apologize if this is a relatively simple question. What's the best way to turn rotational motion into linear motion under the following circumstances? 1. Rotational motion is driven by a vertical bolt. 2. When turned, the bolt will extend a bar...

Homework Statement An object of moment of inertia I is initially at rest. a net torque T accelerates the object to angular velocity omega in time t. The power with which the object is accelerated is? The right answer apparently is [ I * omega^2 ] / [2 * t]. Could anyone please explain why...

Homework Statement A ball rolls down an incline plane without slipping. What is the ratio of its angular velocity at h/3 to its angular velocity at 2h/3? 1) 1:2 2) 1:sqrt(2) 3) 1:1 4) sqrt(2):1 5) 2:1 Homework Equations Conservation of energy with provisions for rotational and...

Hello, I am trying to create a mechanism that will allow for a motor to power a pendulum-like motion (but not an actual pendulum), back and forth. As shown in the picture, I need 180 degrees of rotation about the swinging part. I have researched escapement, but I need this design not to rely on...

So basically, I was doing my AP Physics 1 homework and came across the spinning ice skater question yet again. The question states, "An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the...

So if a ball is rolling down a ramp and not slipping, you have two torques... the mg*sin(theta) portion of gravity and the (mu)mgcos(theta) for friction. My question is this: Does this friction force remove energy from the ball? (I know it affects the balls rotation but this is just changing...

Homework Statement A solid sphere, starting from rest, rotates with constant angular acceleration α about a fixed axis passing through its center. Consider a particle within this sphere that lies at a perpendicular distance r from this axis. If, at some instant, the linear acceleration of this...

Homework Statement A bowling ball is released with speed V and no rotational kinetic energy. After a period of sliding and rotating, the ball enters pure rotational motion. The coefficient of friction between the ball and the ground while sliding is Uk. a. Show that the rotational acceleration...

Homework Statement The problem is attached in the file "selection(1).pdf" The explanations/solutions are attached in "selections.pdf" which is below [Problem image - added by moderator to make it visible in-thread] Looking at how they solved part C, I have no idea why they say that the...

Homework Statement A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed omega_0. It is then lowered, and at the instant its edge touches the ground the speed of the axle is zero. Initially the wheel slips when it touches the...

Homework Statement http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_frq_physics_c_mechanics.pdf The problem is above. It is number 3. The solutions are below: http://media.collegeboard.com/digitalServices/pdf/ap/apcentral/ap13_physics_cm_scoring_guidelines.pdf Homework...

1. Homework Statement A cylinder of mass M and radius R rolls (without slipping) down an inclined plane whose incline angle with the horizontal is theta. Determine the acceleration of the cylinder's center of mass and the minimum coefficient of friction that will allow the cylinder to roll...

Homework Statement A major-League pitcher throws a baseball towards home plate. the ball rotates at 1560 rpms,and it travels 18.5 meters to the plate at an average translational speed of 40.2m/s.how many revolutions does the ball make during this trip? Homework EquationsThe Attempt at a...

Homework Statement https://web.njit.edu/~gary/111/assets/HW10_SOL.pdf'][/PLAIN] https://web.njit.edu/~gary/111/assets/HW10_SOL.pdf The problem is on page 3 of the document along with relevant solutions. Homework Equations F=ma, and Sigma Torques = (moment of inertia) * angular acceleration...