In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.
According to Euler's rotation theorem the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. However, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degrees of freedom.
An example where rotation representation is used is in computer vision, where an automated observer needs to track a target. Consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate system). The basic problem is to specify the orientation of these three unit vectors, and hence the rigid body, with respect to the observer's coordinate system, regarded as a reference placement in space.
Homework Statement
A disk with a radial line painted on it is mounted on an axle perpendicular to it and running through its center. It is initially at rest, with the line at q0 = -90.0°. The disk then undergoes constant angular acceleration. After accelerating for 3.15 s, the reference line...
A rigid body, starting at rest, rotates about a fixed axis with a constant angular acceleration α. Consider a particle a distance r from the axis. Express (a) the radial acceleration and (b) the tangential acceleration of this particle in terms of α, r and time t.
c) if the resultant...
1. A bike is moving at X m/s. Its tires are .60 m in diameter. How fast is a point at the rim of the top of one of the wheels moving relative to the ground?
2. v = r omega, C = 2 pi r (?)
3. At first we thought he just wanted angular velocity. Then when we realized that his given...
A computer disk drive is turned on starting from rest and has constant angular acceleration.
If it took 0.410 s for the drive to make its second complete revolution, how long did it take to make the first complete revolution? What is its angular acceleration, in rad/s^2
I cannot find out...
Homework Statement
A grindstone in the shape of a solid disk with diameter 0.490 m and a mass of m = 50.0 kg is rotating at omega = 890 rev/min. You press an ax against the rim with a normal force of F = 170 N, and the grindstone comes to rest in 7.20 s.
Homework Equations
τ=Iα
ωz=ω0z+μkαt...
A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure. The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m...
Our sun rotates in a circular orbit about the center of the Milky Way Galaxy. The radius of the orbit is 2.2x10^20 m, and the angular speed of the sun is 1.2x10^-15 rad/s. (a) What is the tangential speed of the sun? (b) How long (in years) does it take for the sun to make one revolution around...
Our sun rotates in a circular orbit about the center of the Milky Way Galaxy. The radius of the orbit is 2.2x10^20 m, and the angular speed of the sun is 1.2x10^-15 rad/s. (a) What is the tangential speed of the sun? (b) How long (in years) does it take for the sun to make one revolution around...
This is the latest question I've been stuck on.
The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the n=2 orbit, the distance from the proton to the electron is 21.16e-11 m , and the linear speed of the...
The sun appears to move across the sky, because the Earth spins on its axis. To a person standing on the earth, the sun subtends an angle of sun = 9.30 x 10-3 rad (see Conceptual Example 2). How much time (in seconds) does it take for the sun to move a distance equal to its own diameter...
A 10.7 g CD with a radius of 6.06 cm rotates with an angular speed of 30.9 rad/s. What is its kinetic energy?
What angular speed must the CD have if its kinetic energy is to be doubled? Here is my work:
kinetic energy energy = 1/2 m v2
= 1/2 m ( r ω )2...
so there's a wheel with radius R and mass M. there's also a hub attached to the wheel's center with radius r and mass m. there's also a mass X suspended from a massless string that's wound around the hub. if the axle has negligible radius and mass and both wheel and the hub are solid with...
Hi
I need some help.
The question is:
At the local swimming hole, a favourite trick is to run horizontally of a cliff that is 8.3m above the water. One diver runs off the edge of the cliff, tucks into a ball and rotates on the way down with an average angular speed of 1.6rev/s. Ignore air...
Can anyone help me with these 2 ?
1.) A cd with a diameter of 12 cm, speeds up from 0 to 4 rev/s in 3s. What is the tangential acceleration of a point on the outer rim of the disk at the moment when angular speed is a.) 2 rev/s b.) 3 rev/s
2.) A fisherman reels in a fish and turns the...
Just wanted to check to ensure I have calculated the correct answers for the following question:
A rotating wheel accelerates uniformly at
6.2 rad/s2, and completes 25 revolutions
during a 5.0 s interval. (a) What is the
angular velocity of the wheel at the start of
the 5.0 s interval...
Time Independent Rotational Kinematics equation?
Ok i was trying to figure out the angular acceleration for a problem, but i didn't have the time...so the book said to use the "time independent rotational kinematics equation" but i couldn't find it in the book anywhere or even on the...
Hey all I have a couple questions about some homework that I've been working on...
1 -
The warranty on a new tire says that an automobile can travel for a distance of 98,000 km before the tire wears out. The radius of the tire is 0.35 m. How many revolutions does the tire make before wearing...
A quarterback throws a pass that is a perfect spiral. In other words, the football does not wobble, but spins smoothly about an axis passing through each end of the ball. Suppose the ball spins at 7.04 rev/s. In addition, the ball is thrown with a linear speed of 21.6 m/s at an angle of 47.0°...
A thin rod rotates at a constant angular spped. COnsider the tangential spped of each point on the rod for the case when the axis of rotation is perpendicular to the rod (a) at its center and (b) at one end. Explain for each case whether there are any points on the rod that have the same...
1. A uniform rod of length 3m is suspended at one end so that it can move about an axis perpendicular to its length. The moment of inertia about the end is 6kgm^2 and the mass of the rod is 2kg. If the rod is initially horizontal and then released, find the angular velocity of the rod when
i)...
Hi! I'm not sure where to start on this question and I would be very thankful if somebody could help me on it:
At a mini golf course, a golf ball passes through a windmill. The windmill has 8 blades and rotates at an angular speed of 1.25 rad/s. The opening between successive blades is equal...
This problem is supposed to be easy, but I can't seem to figure it out.
----A bicycle with 62.8cm diameter tires travels 7.90km. How many revolutions do the wheels make? ----
I know I can use the circumference somehow...if anyone can help me out I'd really appreciate it. :)
Hello,
I have a problem where I honestly have no idea how to get started. I have a slight idea what might be invloved but other than that, I am stumped.
Here's the problem: At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 8.6m above the water. One...
rotational kinematics problem I am stuck on please help!
my problem says this:
-a pendulum consisting of a string of length L attached to a bob of mass m swings in a vertical plane. When the string is at an angle Theta to the vertical, A) what ist he tangential component of acceleration of...
Everyone that's taken basic physics know that the kinetic energy of a spinning object with no translational velocity is
KE=(1/2)Iw^2.
where I is the moment of mass and w is the angular velocity. I've been trying to find a similar formula incorporating special relativity but the math is...
Please forgive me if this is sloppy. And sorry for not posting this thread here in the first place (I didn't know about this section of the forums). Thanks in advance for any help you can provide.
A 2.0kg cylinder (radius=.1m and length=.5m) is released from rest at the top of a ramp, and is...
i've been doing some physics problems out of the text and I was wondering: If an electric fan were to be turned off and you knew its angular acceleration, it is possible to find the number of revolutions it makes in a certain time interval?
also, i having a difficult time with this...
The Tub of a washer goes into a spin cycle, starting from rest and gaining angular speed steadily for 8 s, when it is turning at 5 rev/s. At this point the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 12s. Through how many...
hello, i am new to this board. i was having some problems with this problem?
at t = 0 a flywheel is rotating at 50 rpm. A motor gives it a constant acceleration of 0.5 rad/seconds(squared) until it reaches 100 rpm. The motor is then disconnected. How many revolutions are completed at t = 20 s...
A phonograph record slows from an initial 45 rpm at a rate of .05 rad/s^2.
a) how long does it take to come to rest?
orig rotational velocity = 45 rpm = 4.71 rad/sec
acc = -.05 rad/s^2
0 = 4.71 rad/s + (-.050 rad/s^2) t
t = 94.2 s
b) How many revolutions does it make before...
A wheel has eight spokes and a radius of 38.0 cm. It is mounted on a fixed axle and is spinning at 2.80 rev/s. You want to shoot a 27.0 cm long arrow through the wheel, parallel to this axle, without hitting any of the spokes. Assume that the arrow and the spokes are very thin and evenly spaced...