What is Rotational mechanics: Definition and 79 Discussions
Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will appear.
This article assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.
This question is from the Jee Advanced 2017. This question stumped me because it was very difficult to do, the first part of the comprehension was asking for the kinetic energy of the ring.
This is what I mean.
Using the no-slip condition we can write ##\omega R-v_c=\omega_0r##. This is the...
Here is my depiction of the initial state:
Note that the presence of ##f_k## means the ball is initially slipping. We also know that the linear and angular speeds of the ball are increasing in time. At some point, the ball should stop slipping.
The condition for no slipping is that the speed...
In learning about translational and rotational motion, I solved a problem involving a wheel rolling down an inclined plane without slipping.
There are multiple ways to solve this problem, but I want to focus on solutions using energy.
Now to my questions. The reference frame in the posted...
I'm self-studying MIT OCW's 8.01, Introduction to Classical Mechanics Course. I am on the final week, where the topic is translational and rotational motion. I was following along the course notes and reached an example which I'd like to dive a bit deeper into, but I am not sure how.
The problem...
The acceleration and velocity of a body rolling down without slipping on a frictionless inclined plane are given by
$$
a=\dfrac{mg\sin \theta }{m+\dfrac{I}{r^{2}}}=\dfrac{g\sin \theta }{1+\dfrac{K^{2}}{r^{2}}} \cdots(1)
$$
$$...
When one of the pivot is pulled, just at that moment a couple is formed due to the normal reaction from the existing pivot and the weight of the bar. From the assumptions given in the question, we can state that the distance between the two forces (N & W) giving rise to the couple is L/2.
Using...
By solving conservation of energy, I was able to find the linear velocity which is
[10g(H-R-Rsin(theta))/7]^½ and by differentiating this with respect to "t", I arrived at the tangential acceleration value of -(5gcos(theta))/7 and found it to be in agreement with the solution provided in the...
I found out the time when rotation ceases to be 4 ##v_0## /5*mew*g, where mew=coefficent of friction of surface but I am unable to plot the graph post that time
This isn't really a proper homework question, but something I wondered about myself. To simplify things, we say that pivot point is in the origin of a Cartesian coordinate system, and the angles are constrained to the first quadrant.
We see that the weight of the barbell is given as $$F =...
Here I have some problems. I get confused when it says"with respect to the path", is it different from "with respect to the earth"? Because the path is on the Earth. Then, the vehicle is not accelerated in the vertical direction because it moves along the path, is it?
A mass m is tied to a string which is wrapped to a twig of a tree. How many minimum times should we wrap the string so that it doesn't fall?
Here is what i got...
1.There is friction between the twig (or fixed cylinder) and the string.
2. if the total friction between the string wrapped around...
Homework Statement
A uniform cylinder of mass ##M## and radius ##R## is released from rest on a rough inclined surface of inclined surface of inclination ##\theta## with the horizontal as shown in the figure. As the cylinder rolls down the inclined surface, what is the maximum elongation in...
Homework Statement
Homework Equations
Moment of inertia
Torque
Angular momentum
The Attempt at a Solution
I think I can understand the physics of the situation. There will be a torque on the bus due to gravity while the back of it remains in contact with the cliff and it will start to rotate...
Homework Statement
A student throws a stick of length l up in the air .At the moment the stick leaves his hand ,the speed of the stick's end is zero.The stick completes N turns just as it is caught by the student at the initial release point . Show that the height to which the centre of mass...
Homework Statement
Homework Equations
Conservation of linear momentum
Conservation of angular momentum
##\frac{-v_{relative after collision}} {v_{relative before collision}}=e## where e is coefficient of restitution
The Attempt at a Solution
Components of velocity given as...
Homework Statement
A uniform thin rod of length ##2l## and mass ##m## lies on a horizontal table. A horizontal impulse ##J## is given to the rod at one end. There is no friction. The total kinetic energy of the rod after impulse will be ?
Homework Equations
##Jl=I\omega##
##J=mv_{cm}##...
Homework Statement
A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping.
Homework Equations
Since the shell is rolling, friction does not act at the bottom.
So equating the torque,
F*R= I*α
The...
[Note: Post moved to homework forum by mentor]
So I stumbled upon a reviewer for my physics exam tomorrow and I was wondering how the equation was formulated. Your help is very much appreciated :) ! Normally I would consult my professor for this but it's Sunday in my country today so I can't...
Homework Statement
Rods of negligible mass connect discrete masses as shown in the diagram below. For each system, the masses rotate about the midpoint of each connecting rod. Furthermore the systems appear to rotate in unison as time progresses. Do the systems have the same velocity?
Homework...
Homework Statement
"Find the tension in the right string, when the left string is cut, if the mass of the rod is ##m## and its length is ##l##, and ##\sin \theta = 3/5##. The rod is initially horizontal." Please refer the diagram below (sorry for its clumsiness!).
Homework Equations
$$I_{rod}...
i have often come across the sentence "by taking moments" in rotational mechanics, but i really don't understand ,what it is.please explain it(iam not referring to moment of inertia).
1. A ball of mass m is placed in a smooth groove at the centre of disc and the frame starts to rotate with angular speed w, which if the following statement are incorrect?
1) Net force on the ball is towards center.
2) Motion of ball is in radially outward direction w.r.t center.
3)...
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...
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
A uniform solid sphere of radius R rolling on a rough horizontal surface without slipping, with an angular velocity 'w' meets a rough inclined plane of inclination 60degrees. The sphere continues to roll up the plane without slipping with an angular velocity 'n' given by...
Homework Statement
A plank having mass 3.7 kg rides on top of two identical solid cylindrical rollers each having radius 5.5 cm and mass 2.9 kg. The plank is pulled by a constant horizontal force of 6 N applied to its end and perpendicular to the axes of the cylinders(which are parallel)...
Homework Statement
A plank having mass 3.7 kg rides on top of two identical solid cylindrical rollers each having radius 5.5 cm and mass 2.9 kg. The plank is pulled by a constant horizontal force of 6 N applied to its end and perpendicular to the axes of the cylinders(which are parallel)...
Homework Statement
A uniform rod of length "L" is kept vertically on a smooth horizontal surface at a point "O". If it is rotated slightly and released, it falls down on the horizontal surface. To what distance will the lower end of the rod "shift" from point "O" ?
Note : The answer in the...
Hi friends,
Here is a typical problem
https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-ash4/432331_2639240957573_1038427614_n.jpg
It is an elastic collision. Here I am applying simply the conservation of linear momentum as,
Momentum before collision = Momentum after collision
i.e...
Hi friends the problem states like this:
https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-ash3/s480x480/68815_2639239357533_424911713_n.jpg
When the attached block is horizontal it is applying torque on the ring. Here I am using the formula T = Iα
So,
mg. r = (mr2(ring) +...
Hi Friends I am getting some problem in solving this question every time with the help of energy conservation. Please help me out. Here is the question
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn1/s480x480/32407_2637149505288_842292859_n.jpg
Well I am doing that thing ,
By...
Homework Statement
a uniform rod of mass m nd length 2l lies on smooth horizontal surface. a particle of mass m is connected to a string of length l whose other end is connected to one of the ends of the rod. initially string is taut and both string and rod lie in same plane with 90 angle...
Homework Statement
a solid cylinder of mass m and radius R and a plank of mass M are placed on a smooth horizontal surface. there is sufficient friction between the cylinder and the plank's surface to prevent sliding of the cylinder. the fixed pulley is smooth. if the plank is pulled with a...
Hi,
I see in many of these physics problems it is explicitly stated that "the cord on the pulley does not slip." [1] What is the implication of this? Why is it important?
Also, there is a problem here with a diagram that I will try to explain in words and then have a question about...
Homework Statement
Hello everyone,
Please help me with this problem, as I am getting stuck solving this problem.
A solid sphere of Mass M and Radius R rolling (pure) encounters a protrusion on the surface of height R/4. Its in the form of a step. What can be the maximum velocity V of...
Hello everyone,
Please help me with this problem, as I am getting stuck solving this problem.
A solid sphere of Mass M and Radius R rolling (pure) encounters a protrusion on the surface of height R/4. Its in the form of a step. What can be the maximum velocity V of...
Two solid cylinders p and Q of same mass and same radius start rolling down a fixed inclinded plane from the same height at the asme time.cylinder P has most of its mass concentrated near its surface while Q HAS MOST of its mass near the axis...
THEN
1)WHICH HAS MORE MOMENT OF INERTIA AND...
Homework Statement
The problem is attached as an image. Note this is from a past exam.
Homework Equations
Conservation of angular momentum.
Rotational kinetic energy.
The Attempt at a Solution
a) The moment of inertia of the man and stool is given as 3 kg m^2, and the dumbells...
This is an example problem I am studying from a classical mechanics textbook.
Wrap a light, flexible cable around a solid cylinder with mass M and radius R. The cylinder rotates with negligible friction about a stationary horizontal axis. Tie the free end of the cable to a block of mass m and...
I have the working for part d) but I don't understand certain parts, so my problems lie with part d), f) and g)
Homework Statement
3. A solid wooden disk is suspended as shown: it has mass 7.70 kg and radius
0.219 m . It is rotated from rest about its vertical axis, reaching an angular...
In rotational mechanics i am mostly confused with the axis of rotation. Let me give you some examples of question.
about which axis. Is that instantaneous axis of rotation.
OK this may seem to be solved here but what about this question.
Now once again. which axis should i choose...
One more question on rotation.
first of all see attachment i want to say that if friction is too large then net force is in direction of inclined in upward direction but from common experience we can say that it will move in downward direction so where is it going wrong. why it moves in...
Homework Statement
A cubical block of mass 'm' and edge length 'a' slides down a rough inclined plane of inclination alpha radian with a uniform speed. Find the torque of the normal force acting on the block about its center.
On the back of the book answer is \frac{1}{2}mga sin(alpha)
2. The...
Rotational mechanics...
Homework Statement
This is actually a simple harmonic motion question but the doubt i have is with a concept in rotation...
I will state the exact problem...
A solid sphere(radius R) rolls without slipping in a cylindrical trough(Radius 5R).
Find the time period of...