What is Rotational dynamics: Definition and 271 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.
I am right now studying Rigid Body dynamics..
I have some doubts regarding Dynamics...
1) When a body is rotating as well as translating...we say that every particle of the ..lets say ROD is moving with a resultant velocity = Vcm ( translational velocity of COM) + ω.R (where R is the...
Hi friend I am really getting big problem in solving this question which is related to Rotational dynamics. Please help me in solving this. I will be heartily thankful to u all guys.
The question is as follows ...
Hi, I'm new to the forum, starting off with some rotational stuff that I am not grasping well...
I have diagrams for each question too, which i feel are vital to understanding the questions
Homework Statement
A spherical ball bearing 0.025m in diameter, rolls without slipping down an...
Homework Statement
A plank with a mass M = 6.10 kg rides on top of two identical, solid, cylindrical rollers that have R = 4.10 cm and m = 2.00 kg. The plank is pulled by a constant horizontal force F of magnitude 4.80 N applied to the end of the plank and perpendicular to the axes of the...
Homework Statement
I've been trying to attempt this problem for the past day but I don't understand how to answer the questions. It's frustrating. If someone could point me in the right direction that would be nice. My TA did the problem in class but I still don't quite understand it. This is...
Homework Statement
A man drags a 71.5-kg crate across the floor at a constant velocity by pulling on a strap attached to the bottom of the crate. The crate is tilted 22.5° above the horizontal, and the strap is inclined 64.0° above the horizontal. The center of gravity of the crate coincides...
Homework Statement
A uniform sign is nailed into a wall at its top two corners. The nail on the upper-right corner breaks, and the sign begins to rotate about the remaining nail in the upper-left corner. The mass of the sign is 69 kg, L (length) = 1.6 m, H (height) = 2.2 m, and the moment of...
So I've been prepping for my Engineering Physics 1 final, and I've been having trouble with rotational motion problems, but this problem has been driving me crazy for the past two days:
Homework Statement
(I wanted to include a normal link to an image, but I'm a new member, so here's...
Hi all, first year MechEng student here, final question of the final assignment of the year, would appreciate any assistance:
Homework Statement
A 0.150 kg yo-yo has an outer radius R that is 5.60 times greater than the radius r of its axle. The yo-yo is in equilibrium if a mass m is...
a) suppose we tie a ball with a string and rotate it keeping its other end tied with one of our fingers then the only external force acting on it is the tension. Which force then cancells 'mg' acting vertically downward?
b) if a mass is rotating in a circular path then in which direction does...
Homework Statement
http://imageshack.us/photo/my-images/545/rotacion1.jpg/
Translation: Determinate, for the system of Fig. 10-39 the angular velocity of the disk and the linear velocity of m and m'. Calculate the tension in each string. Suposse that m = 600 g, m' = 500 g, M = 800 g, R = 8...
Homework Statement
A uniform thin rod of weight W = 100 N is supported horizontally by two vertical
props at its ends. At time t = 0 one of the these supports is kicked out. Find the
force on the other support immediately thereafter.
Homework Equations
F1 + F2 = mg
The Attempt...
Homework Statement
A dumbbell is made of a rod length L and mass M, and 2 spheres of radius r and mass m (see figure). The rod is attached at a distance L/3 from the left end to a
rotational axis A. The dumbbell is let go under gravity and makes a rotational motion under gravity around the...
Homework Statement
There is a dumbbell with two masses attached at each end, rotating about a point. The distance between the two masses is R, and the two masses do not have the same mass. m1 < m2
If the angular velocity ω is held constant, by what factor must R change to double the...
problem 1:
Homework Statement
this isn't quite a problem but a general confusion about how to setup the problem. for example:
a cylinder of radius R with mass M has a force T applied at its center of mass, pointing horizontally to the right. assuming the cylinder only rolls without...
Homework Statement
A bicycle wheel has a diameter of 63.8 cm and a mass of 1.79 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire...
Homework Statement
** disregard A)
http://img153.imageshack.us/img153/917/img20111024001591.jpg
Homework Equations
T= Fd
The Attempt at a Solution
[PLAIN][PLAIN]http://img21.imageshack.us/img21/9645/img20111024001611.jpg
Basically I'm stuck now, and don't know what to do.. I...
Homework Statement
A uniform, solid cylinder with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M...
Homework Statement
http://i.imgur.com/2Pi18.png
Homework Equations
The Attempt at a Solution
Sorry to say this, but I am completely clueless about these questions. I don't know how to start what to consider. Would anyone like to help me?
Thanks!
Homework Statement
A spherical body is rolling on a rough surface.
then "the frictional force may or may not be zero"
Is this statement is correct or not?
we discussed about this in classroom.
Some were saying it must not be zero and others were saying it may be zero.
Which is correct?
In a class demonstration, a bicycle wheel was held on an axle and spun. The result came to be that the wheel while rotating held a vertical position while holding it by a string attached to the end of the axle. After the wheel stopped rotating its vertical position ceased and the wheel attained...
Homework Statement
A grinding wheel is a uniform cylinder of with a radius of 8.50 cm and a mass of 0.580 kg. Calculate a) its moment of inertia about its center, and b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.0 s if it is known to slow down from 1500 rpm to rest...
Homework Statement
A plyground merry go round of radius r=2m had a moment of inertia of I=250kg/m2 and is rotating at 10rpm about a frictionless verticle axle.Facing the axle a 25kg child hops onto the merry go round and manages to sit down on its edge.What is the new angular speed of the...
Homework Statement
A uniform solid cylinder and a uniform cylindrical shell are placed side by side at the top of an incline.If they sre released from rest and roll without slipping,
A)Determine their speeds when they reach the bottom
B)Which objet reaches the bottom first?
Homework...
Homework Statement
An inelastic uniform solid sphere of radius 'R' is sliding without rolling over a frictionless ground with a uniform velocity 'v'. A cubical plate of height r (r<R) is fixed on the ground and the sphere impinges upon the cubical plate and rolls over it. What is the minimum...
Homework Statement
We have a rod length l with mass m. This rod is nail at its end to a wall. A putty with mass m also then collide with the rod right at the other end. The collision is perpendicular to the rod.
Question is what is the minimum velocity the putty need to travel to rotate the...
Homework Statement
A block of mass m = 9.00 kg is situated on an incline of angle θ = 51.0^{\circ} with coefficient of kinetic friction \mu_k = 0.200, and is connected to a light spring of spring constant k = 40.0 N/m via a light rope passing over a massive pulley as shown. The block is...
Homework Statement
A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T. The walls of the cone make an angle B with the vertical. The coefficient of static friction is between the block and...
Homework Statement
A thin plank of mass M and length l is pivoted at one end. The plank is released at 60 degrees from the vertical. What is the magnitiude and direction of the force on the pivot when the plank is horizontal.
Homework Equations
N/A
The Attempt at a Solution
So...
1. Homework Statement [/b]
A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T. The walls of the cone make an angle v with the vertical. The coefficient of static friction is between the...
Can anyone help me figure out this question? I swear this isn't homework! I am actually from a car forum and would like to understand some basic principles behind car engine pulleys.
Pulley A drives another pulley Bx via a belt.
Pulley A
diameter:15inches
weight: 1lbs
applied torque...
I misunderstood the problem, and the answer is the correct one! sorry, and someone can close this post if necessary
Homework Statement
A stick of uniform density with mass M = 7.9 kg and length L = 1 m is pivoted about an axle which is perpendicular to its length and located 0.15 m from one...
I have been working on a dynamometer project for radio controlled cars. You can see my early (and somewhat crude) attempts here: http://www.youtube.com/watch?v=qEhnFd8bwqM"
A question has come up in some of the discussions I have had with other enthusiasts. Given the diameter of the rollers...
Homework Statement
2 children, masses 35kg and 40kg sit at opposite ends of a 3.4m seesaw with mass 25kg with the fulcrum at midpoint. with the seesaw horizontal find
a) the net torque
b)angular acceleration
Homework Equations
tau=rF=Ialpha
The Attempt at a Solution
i got the right...
I don't get the right hand rule that apply to rotational dynamics. How could I use to solve a torque problem and how to know when its positive and what is negative.
Homework Statement
A diver of weight 582 N stands at the end of a uniform 4.48-m diving board of weight 142N The board is attached by two pedestals 1.55 m apart. Find the tension in each of the two pedestals.
Homework Equations
Torque= force x distance
Torque = Rotational Interia x...
rotational dynamics rod--please help!
Homework Statement
A thin rod of length l and mass m is fixed at a far ends by a free pivot and held from rotating with a string attached at 3/4l and fixed toa ceiling. The moment of inertia of a thin rod about a far end is ml2/3
a) what is the pivot...
Hi guys,
I have a question. I have lived life in the apparent belief that if a car is moving at a fast enough speed, turning it's wheel becomes increasingly difficult. Could somebody explain that concept to me? I assume it has something to do with the angular momentum of the wheel to make the...
how do you do part c, d, and e
A string is wrapped several times around the rim of a small hoop of radius 0.0690 m and a mass 0.152 kg. The situation is sketched in the figure below.
If the free end of the string is held in place and the hoop is released from rest, calculate the following...
How do you find the minimum coefficient of friction needed to prevent slipping for part a and part b.
A hollow spherical shell of mass 4.00 kg rolls without slipping down a 38.0° slope.
(a) Find the acceleration.
3.62 m/s2
Find the friction force.
9.64 N
Find...
Homework Statement
A large hollow hamster ball is rolling along the ground at 5 miles per hour. A hamster is running inside, matching his pace at the bottom of the ball to stay by the ground. The hamster weighs .3 kg, and the ball has a mass of 1.5 kg with a radius of 0.4m.
Homework...
Homework Statement
The leaning Tower of Pisa (Fig. 9-47) is 55 m high and 7.0 m in diameter. The top of the tower is displaced 4.5 m from the vertical. Treat the tower as a uniform, circular cylinder.
(a) What additional displacement, measured at the top, will bring the tower to the...
Homework Statement
A solid sphere starts from rest at the upper end of the track, as shown in figure below, and rolls without slipping until it rolls off the right-hand end. If H = 12.0 m and h = 2.0 m and the track is horizontal at the right-hand end, how far horizontally from point A does...
I have been trying to get ready for my final and rotational dynamics seems to be very difficult for me. I have read the book and feel like I am just not comprehending what the concepts are. Here is a problem I am stuck on.
A uniform board is leaning against a smooth vertical wall. The...
Homework Statement
Two weights are connected by a very light flexible cord that passes over a 50 N frictionless pulley of radius .300 m. Pulley is a solid uniform disk and is supported by a hook connected to a ceiling. What force does the ceiling exert on the hook? There are two weights...
A uniform solid sphere of mass M and radius R rolls, without slipping, down a ramp that makes an angle θ with the horizontal.
The question ask for me to find the force of friction between the ramp and the sphere.
My attempt at the problem was to utilize the x-component of the force of gravity...
Ok i am not good with physics and these are some review problems for my test coming up. Please help.
At time t1 = 0 an electric grinding wheel has an angular velocity of 28.0 rad/s. It has a
constant angular acceleration of 32.0 rad/s2. At time t2 = 2.20 s a circuit breaker trips, and the...
Homework Statement
You have a flywheel rotating at 1000rpm. It has a moment of inertia of 0.5 Kgm^2 and a diameter of 0.5m.
It is unclear if you know the mass. You know the moment of inertia, which is calculated using mass, but whilst the flywheel is circular I'm not sure that the surface...
1. A wheel of mass M and radius of gyration "k" spins on a fixed horizontal axle passing through its hub. Assume that the hub rubs the axle of radius "a" at only the top-most point, the coefficient of kinetic friction being μk. The wheel is given an initial angular velocity Wo. Assume uniform...
Homework Statement
You have a rectangular frame with side lengths l and l', and a rigid rod attached to this frame at two points, r1 and -r1. The rod passes through the center of mass, and makes an angle theta with the horizontal. Then you begin to rotate the the frame around the rod with...