What is Rotational dynamics: Definition and 270 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.
Homework Statement
A common physics demonstration consists of a ball resting at the end of a board of length L that is elevated at an angle of theta with the horizontal. A light cup is attached to the board at Rc (Rc is a distance up the board from the bottom, it is not past the support...
Hi all,
I've got a question that I'm stuck on.
Three disks are spinning independently on the same axle without friction. Their respective rotational inertias and angular speeds are I,w (clockwise); 2I,3w (counterclockwise); and 4I,w/2 (clockwise). The disks then slide together and stick...
There is this problem that I am having trouble with, can someone guide me through this problem. Thanks
http://img227.imageshack.us/img227/2681/scan0003eq3.png
Homework Statement
A solid ball, with radius r = 6.00 centimeters and mass m = 0.400 kg, rolls without slipping on the inside of a fixed horizontal circular pipe with radius R = 0.300 meters. The ball is held at rest with its center lying on the horizontal diameter of the pipe. It is then...
Homework Statement
Two cars race around a circular track. Car A accelerates at 0.340 rad/s2 around the track, and car B at 0.270 rad/s2. They start at the same place on the track and car A let's the slower-to-accelerate car B start first. Car B starts at time t = 0. When car A starts, car B...
Homework Statement
The descending pulley shown in the figure has a radius 20 cm and moment of inertia 0.2 kg m^{2}. The fixed pulley is light and the horizontal plane frictionless.
Find the acceleration of the block if its mass is One kg...
Homework Statement
A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. How much string has unwrapped from...
I'm sure there is something ridiculously simple I'm missing here but this questions has been driving me crazy and now I'm sure I couldn't see the answer if it stared me right in the face.
Homework Statement
A massless string is wrapped around a solid cylinder. A block of mass m=2.0kg...
Hi. I've been having trouble with 2 problems and I've worked them both 2 or 3 times. Here's my problems and my work. Any help will be greatly appreciated.
1.
Homework Statement
In San Francisco a very simple technique is used to turn around a cable car when it reaches the end of its...
Homework Statement
A uniform plate of mass m is suspended in the way shown. determine immediately after the connection at B has been released ;:
A) angular aceleration of plate
B) acceleration of its centre of mass
Homework Equations
before b is detached
t1 + t2 = mg (Linear equillibrium)
t1...
Homework Statement
A ring (hollow cylinder) of mass 2.30 kg, inner radius 4.35 cm, and outer radius 5.65 cm rolls (without slipping) up an inclined plane that makes an angle of θ=38.0°, as shown in the figure attached.
At the moment the ring is at position x = 1.95 m up the plane, its...
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
wheel then turns through another 350 rad as it coasts to a stop at constant angular acceleration.
(i)...
Homework Statement
A meter stick of mass .44 kg rotates, in the horizontal plane, about a vertical axis passing thru the 30 cm mark. What is the moment of inertia of the stick? Treat it as a long uniform rod.
Homework Equations
I=1/2M(R^2)
The Attempt at a Solution...
[b]1. Judy rides a 2m radius merry-go-round near its edge. Judy has a mass of 100 kg and the merry go round has a mass of 200 kg and rotates at 1 rad/s. What will the new angular velocity of the merry go round be if judy moves 45 percent of the way towards the center?
2.How much tension...
[SOLVED] rotational dynamics
Homework Statement
A thin uniform rod has length 2.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest as angle theta=40 above the horizontal. Use the principle of conservation of energy to determine the angular...
Hello. I have what I hope to be a simple question. It's something that I've come across in several problems in my engineering and physics subjects and I'm not sure exactly what relationship applies. My textbook doesn't seem to be very helpful in the matter.
When there are two circles, I...
An electric-generator turbine spins at 3600 rpm. Friction is so small that it takes the turbine 10.0 min to coast to a stop. How many revolutions does it make wile stopping?
Homework Statement
A wheel initially rotates counterclockwise about a fixed axis, with an initial angular speed of 1.2 radians per second. If it accelerates uniformly to 2.0 radians per second clockwise during a 5 second interval, what is the magnitude of its displacement during this...
Homework Statement
0.14 meter long, 0.15 kg thin rigid rod has a small 0.22 kg mass stuck on one of its ends and a small 0.080 kg mass stuck on the other end. The rod rotates at 1.7 rad/s through its physical center without friction. What is the magnitude of the angular momentum of the system...
My AP Physics C class has a test tomorrow about Rotation Dynamics and my teacher gave us a practive exam over the weekend and i felt really good about it thinking i was going to do really well, but this practice exam is really difficult and I am stuck on every problem. there are four problems...
Homework Statement
Two thin rectangular sheets (0.20 m x 0.43 m) are identical. In the first sheet the axis of rotation lies along the 0.20-m side, and in the second it lies along the 0.43-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its...
Homework Statement
A cylindrical rod 26.0 cm long with a mass of 1.20 kg and a radius of 1.50 cm has a ball of diameter of 7.80 cm and a mass of 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top. The apparatus is free to pivot about the...
On this assignment I could do most of the work easily, I just have some questions on three problems
3. Homework Statement
A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 270 kg·m2 and is rotating at 9.0 rev/min about a frictionless vertical axle. Facing the axle, a...
Homework Statement
A bug of mass 10.0 g stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 50.0g and is 100 cm in length...
[SOLVED] Last 3 problems on Rotational Dynamics
OK, I've done problems 1-3, but I'm having a real hard time with 4-6. Any help you guys could give me would be greatly appreciated!
4. Homework Statement
A block of mass m1 = 2.45 kg and a block of mass m2 = 5.55 kg are connected by a...
A potter is shaping a bowl on a potters wheel rotating at constant angular speed. The frictional force between her hands and the clay is 1.5N total. A. How large is her torque on the wheel, if the diameter of the bowl is 12 cm? B. How long would it take for the potters wheel to stop if the only...
Please help with this question. I don't know how to approach this difficult question
a crossing guard holds a STOP sign at arm's length, as shown. Her arm is horizontal, and we assume that the deltoid muscle is the only muscle supporting her arm. The wright of her upper arm is Wu = 18 N, the...
The Question:
A potter's wheel having a radius of 0.50 m and a moment of inertia of 12 kg m^2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 sec by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of...
Homework Statement
The four particles shown below are connected by rigid rods of negligible mass where y = 5.70 m. The origin is at the center of the rectangle.
(a) If the system rotates in the xy plane about the z axis with an angular speed of 6.30 rad/s, calculate the moment of inertia of...
What minimum force F applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h? Take r as the radius of the wheel and W as its weight.
We know torque is equal to the radius x perpendicular force
T = rFnet
I think I have to find angular...
A uniform board of mass m and length L is pivoted on one end and is supported in the horizontal position by a rope attached to the other end. Another rope, attached to the board a distance L/3 from the pivot point, is being pulled straight down with a constant force of magnitude F.
1) How far...
A massless string is wrapped around a solid cylinder. A block of mass m=2.0 kg hangs from the string. When released, the block falls a distance 82 cm in 2.0 s. Calculate the mass of the cylinder.
Okay, for this problem, I started off with drawing free body diagrams for the block and the...
Greets all, I'm attempting to build a small physics engine that manages linear and angular forces. Please bear with me while I explain the problem I'm having.
Linear forces so far have not been an issue at all, however rotational forces are rather confusing.
I'm using Chris Hecker's rigid...
Homework Statement
A 10kg objects rotates on a point on a wire 3 meters long at the rate of 120 rad/sec without breaking the wire.
1) What is the numeric value (and units) of the velocity vector and 2)what angle does it make with the tangent at any point? and 3) What's the minimum tensile...
Homework Statement
Does anyone know of a treatment of rotational dynamics especially the heavy top and precession of the equinoxes which uses only vectors and tensors. I've got treatments in terms of Lagrange's equations, but I wanted something using only torques etc.
Homework Equations...
[/B]1. Homework Statement [/b]
A cat walks along a uniform plank that is 4.00 m long and has a mass of 7.00 kg. The plank is supported by two sawhorses, one 0.44 m from the left end of the board and the other 1.58 m from its right end. When the cat nears the right end, the plank just begins to...
Homework Statement
Question Details:
A 10 kg engine is rotating at the rate of 20 rad/sec about a point on a wire 3 meters in length with a working tensile strength of 1.8*106 N. The engine is fired and produces an acceleration of 1 rad/sec2. What's the maximum possible ω (angular velocity)...
Homework Statement
Problem: A massless string is wrapped around a solid cylinder as shown in the diagram at the right. A block of mass m = 2.0 kg hangs from the string. When released, the block falls a distance of 82 cm in 2.0 s. Starting with a free-body diagram, calculate the mass of the...
Homework Statement
A wheel is turning initially at 1200 turns/min and stops in 4 min because of friction. If we add a supplementary torque of 300 N*m, the wheel stops in 1 min.
a) What is the moment of inertia of the wheel?
b) What is the torque of friction?
Homework Equations
Torque...
Homework Statement
Find the rotational acceleration, final tangential velocity and centripetal acceleration of a 50.0 g rubber bung, starting from rest, swung in a horizontal circular path on a very light string of length 90.0 cm. The tension in the string is provided by a mass of 250.0 g...
I have a quiz tommorrow and i am reviewing the harder problems and i can't get started on this one
A bicycle Wheel is resting against a small step whose height is h=0.120 m. The weight and radius of the whell are W=25.0N and r=0.340 m. A horizontal force F is applied to the axle of the...
Hello, I know the rules state to show work to receive help but my problem is that i don't know where to begin so i am lookign for a push in the right direction...here is the question...
A lunch tray is being held in one hand, as the figure illustrates. The mass of the tray itself is 0.200 kg...
In Fig. 10-35, two particles, each with mass m = 2.30 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 0.670 m and mass M = 0.360 kg. The combination rotates around the rotation axis with angular speed ω = 0.211 rad/s. Measured about O, what are...
A Right Circular uniform Solid cone of mass m and semi vertical angle a(alpha) is placed over a rough horizontal surface. Assuming friction to be sufficient to prevent slipping, find the minimum force that can be applied at the tip of the cone such that it just topples.
Hello,
I was able to solve this problem fine, but I had a question about it:
"A disk 8.00 cm in radius rotates at a constant rate of 1200 rev/min about its central axis. Determine (a) its angular speed, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial...
dear guys,
i am very depressed since i cannot do these problems...please help me with them..
1)a solid cylinder of mass 20kg and radius 0.12m rotating with initial angular speed of 125ms-2 is placed lightly(ie without any translational push) on a horizontal table with co-efficient of kinectic...
Hey guys, i don't know why its always two or three problems on my homework that always stump me. Any help and tips are appreciated
1) A wheel with a weight of 393N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at an angular...
Can anyone help me with where to begin ? ? ?
Turning a doorknob through 1/6 of a revolution requires 0.1 J of work. What is the torque required to turn the doorknob?
i know that T = F x r
what is the force and radius ?(is radius 3/6=1/2??)
I guess I'll introduce myself as well:
My name is, well, my username, but you can call me Drew (most people do). I'm 18 (a senior in high school) and in an AP Physics II class focusing on mechanics. I posted something in the advanced physics forum that should probably have been moved here, so...
A skinny student (40 kg) sits on a stool that can rotate, holding two 8 kg bowling balls with his arms out stretched. The stool weighs 20 kg. The student and stool are spun such that they have an angular velocity of 2 rad.s-1.
When the student pulls his arms in towards him, what happens to...