What is Rotational: Definition and 1000 Discussions
A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.
Homework Statement
A mass M slides down a smooth surface from height h and collides inelastically with the lower end of a rod that is free to rotate about a fixed axis at P as shown below. The mass of the rod is also M, the length is L, and the moment of inertia about P is ML2/3.
The angular...
Thinking about rotating mass (for example a bike tire) and the disadvantages / advantages that come with differing weights/masses. Most everybody you speak to are programmed to think that a lighter tire will require less energy, thus, everyone tries to find the lightest tire possible...
We are doing rotational volume in Calculus II right now. I know the basic rules for the disk, washer, and shell methods, but I'm having trouble getting started with these questions. I'm not sure how to set up the equations. Any sort of help would be great.
Thanks so much!
Hey,
We saw in class that rotating a spin state with an angle of 2pi returns minus the state, and so it has to be rotated 4pi rad in order to return to the original state.
However, we also saw that the expected value of the spin DOES return to its original value after a rotation of 2pi rad...
rotational motion and moment of inertia---HELP!
Homework Statement
Two masses m1=2.00 kg and m2=1.00 kg are linked by a thread and thrown over a pulley whose mass is 1.00 kg. The radius of the pulley is 0.200 m.
a) Find the acceleration a with which the weights move
b) the tensions T1...
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...
Homework Statement
Imagine a system consisting of a chain that runs over two sprockets. The chain rotates around the sprockets with a constant linear velocity (i.e. the chain is taut and rigid). The front sprocket has a radius rfront and an angular speed ωfront and the rear sprocket has a...
Homework Statement
A diatomic molecule can be modeled as two point masses, m1 and m2, slightly separated. If the molecule is oriented along the y-axis, it has kinetic energy K when it spins about the x-axis. What will its kinetic energy (in terms of K) be if it spins at the same angular...
Homework Statement
Which of the following formulas is valid if the angular acceleration of an object is not constant? Explain your reasoning in each case.
(a) v = rω;
(b) atan = r\alpha;
(c) ω = ω0 + \alphat;
(d) arad = rω2;
(e) K = 0.5Iω2.
Homework Equations
The Attempt at a...
Homework Statement
A 4 kg block, 10m above the ground is attached to a long cord which is wrapped around a 1050 g iron disc of radius 40 cm. The system is originally at rest, afterwards the block is let go and allowed to fall. From the time the block is let go to when the block crashes with...
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...
Hi all, this is not actually homework or similar but the board seemed as the appropriate place for the question.
I have an arm of 1m length pointing upwards from a rotation axis, on the end of the arm is a mass of 1kg, upon release the arm starts rotating downwards due to gravity (no other...
This is a spoiler for all Artificial gravity space crafts. If somebody thinks that he can do whatever he can on earth, on the Space Craft, then here is bad news:
No football, no soccer, no cricket, no birds can exist on the craft without confusion. :confused:
Here is why:
A projectile...
Homework Statement
A solid steel sphere of radius 10 cm and a mass of 1.5 kg rolls down a 1.25 m incline that makes an angle of 20 degrees with the horizontal. Calculate the linear velocity of the following points relative to the ground, when it reaches the bottom of the incline.
a) The...
1. A uniform rigid rod of length L and mass M is attached to a frictionless pivot point at one end. The rod is initially held completely horizontal and is released from rest. What is the linear and angular velocities at the instant the rod is in the vertical position?2. -ΔU = ΔK
3. -ΔU =...
Homework Statement
A rotating bicycle wheel has an angular speed of 2.84 rad/s at some instant of time. It is then given an angular acceleration of 1.75 rad/s2. A chalk line drawn on the wheel is horizontal at t = 0. What angle does this line make with its original direction at t = 1.77 s...
Homework Statement
A block slides down a frictionless half-pipe (shown on the back of this page). It is released from rest at the point (2,0).
Determine the velocity, tangential accleration, radial acceleration and angular acceleration when the block goes through angular displacements of 30...
Hi there,
I posted essentially this question a quite awhile ago but the answer wasn't what I needed and then the post got hijacked so I'll try this again worded differently...
I need to figure out the torque and hp required to rotate a steel drum, both for acceleration and to maintain its...
Homework Statement
This is not a homework question, I was just curious.
I'm trying to find the angle θ that an unbalanced arm produces in the following case:
Homework Equations
τ=rF
The Attempt at a Solution
τ1=τ2
rF=rF
r(98 N)(cos θ)=r(49 N)(cos θ)
However, the cos θ...
Its not actually a homework . i am just wondering .
If we have 2 masses M and m where m rotates about M on either orbit1 of radius R with speed V or orbit 2 of radius r with seepd v , wouldn't its speed ratio V/v equal the following
V/v = (sqrt(GM/R))/(sqrt(GM/r)) where G is gravitation...
Homework Statement
I have a wheel with a diameter of 1.4m and the radius of gyration is 0.42m. The wheel has a mass of 13kg. Calculate maximum rotational kinetic energy.
Homework Equations
The Attempt at a Solution
From this all i can do is calculate the moment of inertia which...
Homework Statement
Consider a small box of mass m sitting on a wedge with an angle θ and fixed to a spring
with a spring constant k and a length in a non-stretched state L. The wedge
rotates with an angular velocity ω around the vertical axis. Find the equilibrium
position of the box...
Homework Statement
4. (9) On an old style record turntable a small rubber wheel is used to drive the larger platter. They are mounted so that their circular edges touch and do not slip while in motion. The small wheel has a radius of 2.0 cm and accelerates at the rate of 3.5 rad/s2 while it...
1. I'm doing an experiment where I have a brass hollow cylinder, and I roll it down an inclined plane, and after each trial, I add fish weights to the inside of it to increase the mass.
I'm testing the proportionality between mass and angular velocity, with my hypothesis being an inverse...
An green hoop with mass mh = 2.4 kg and radius Rh = 0.18 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.4 kg and radius Rd = 0.09 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that...
Hi, I'd like to know the solutions for these equations, and how to arrive at them. Is it possible to derive the general form of F(x,y,z) analytically? I'm still studying linear differential equations so I have no clue on what to do with partial differential equations...
div F = 0
curl F = 0...
we have in rotational motion a=rω,where r and ω are the radius of rotation and angular velocity respectively.What is a (tangential acceleration or centripetal acceleration)
A thin spherical shell lying on a rough horizontal floor is hit by a cue in such a way that the line of action of force passes through the centre.so there is no torque and it moves with a linear velocity V and no angular velocity.the linear velo is to be founded when the shell starts purely...
Homework Statement
Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rappelling). They do this with their body nearly horizontal and their feet pushing against the cliff. Suppose that an 82.0 kg climber who is 1.90m tall and has a center of gravity...
Homework Statement
Flywheels are large massive wheels (disks) used to store energy. They can be spun up slowly, and then the wheel’s energy can be released quickly to accomplish a task that demands high power. A large flywheel has a 2.4 m diameter and a mass of 300 kg. Its maximum angular...
Homework Statement
A juggler is able to handle four balls simultaneously. He takes 0.5 s to cycle each
ball through his hands, throw the ball, and be ready to catch the next ball. (a)
With what velocity must he throw each ball up? (b) What is the position of the
other three balls when he...
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...
A solid sphere of mass m is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup.
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...
A horizontal vinyl record of mass 0.10 kg and radius 0.1 m rotates freely about a vertical axis through its center with an angular speed of 4.7 rad/s. The rotational inertia of the record about its axis of rotation is 0.0005 kg*m^2. A wad of wet putty of mass 0.020 kg drops vertically onto the...
Homework Statement
A whee and axle having a total moment of inertia of .0002 kg*m^2 is caused to rotate about a horizontal axis by means of an 800g mass attached to a cord wrapped around the axle. The radius of the axle is 2 cm. Starting from rest, how far must the mass fall to give the wheel...
Hi everybody,
This is my first post in this forum although I started following it some time ago. My question is related to rotational properties involving harmonic oscillator model.
Homework Statement
We are told to evaluate the expectation value of the rotational constant of a...
Homework Statement
The picture shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0.7 m, its inner radius R1 is R2/2, its mass M is 7.3 kg, and the mass of the crossbars at its center is negligible. It initially rotates at an angular...
Two points are on a disk that rotates about an axis perpendicular to the plane of the disk at its center. Point B is 2.00 times as far from the axis as point A.
If the linear speed of point is V, then the linear speed of point A is
I know the speed of A must be less and i think its V/4. Is...
Two identical merry-go-rounds are rotating at the same speed. One is crowded with riding children; the other is nearly empty.
If both merry-go-rounds cut off their motors at the same time and coast to a stop, slowed only by friction (which you can assume is the same for both merry-go-rounds)...
If we have a ball rolling down from inclined roof that has bottom part at certain height about the ground. I want to know where does the ball land after it leaves the roof. So at this point potential energy is transferred to kinetic (rotational + translational).
My question is: What is the...
This isn't really a homework problem, more of a "I'm-building-something-and-need-to-make-sure-the-physics-are-right-before-I-build-something-impractical" problem.
Homework Statement
Homework Equations
The Attempt at a Solution
(I grouped it all together, easier for me to not separate each...
Homework Statement
Attached is a photo of the linear and rotational dynamics exercises. Times t1 and t2 were measured. For the linear exercise the top block was pushed with an initial force along the FRICTIONLESS level plane. It passed the timing device twice. Once through and once on the way...
Rotational Inertia "Four point masses problem--diagonal"
Homework Statement
Four point masses of 3.0 kg each are arranged in a square on mass-less rod. The length of a side of the square is .50 m. What is the rotational Inertia for rotation about an axis passing through masses A and C...
Homework Statement
A turntable must spin at 33.3RPM (3.49 rev/s) to play an old fashioned vinyl record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 2 revolutions, starting from rest? The turntable is a uniform disk of diameter .305m and mass...
Homework Statement
A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is a) mass and b) rotational inertia if the child's ball reduced compared with the adult ball...
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...
Homework Statement
Give two reasons why as molecular size increases does it become increasingly difficult to experimentally obtain well-resolved rotational spectra?
The Attempt at a Solution
Basically I know one reason. The energy levels become more tightly packed.
I have another...
1. Homework Statement :
I have the momentum acting on the center of mass of a rigid body consisting of 3 bodies.
I would like to have the corresponding rotational forces (of this momentum) on the 3 bodies.
2.
I derive the general form:
Frot_i= Inertia_i*(RixM)/Total_Inertia*(Ri)^2...
I need help with this physics problem! Please help I'm completely stuck.
A beam 3m long is free to pivot up and down about the end attached to a wall. The mass of the beam is 25 kg and the cable supporting the beam can support a maximum force of 1800 N. What is the maximum mass that a man...