What is Rotational kinematics: Definition and 131 Discussions
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.
A jet is circling an airport control tower at a distance of 18.0 km. An observer in the tower watches the jet cross in front of the moon. As seen from the tower, the moon substends an angle of 9.04 x 10-3 radians. Find the distance traveled (IN METERS) by the jet as the observer watches the nose...
Homework Statement
A ball attached to a string starts at rest and undergoes a constant angular acceleration as it
travels in a horizontal circle of radius 0.30 m. After 0.65 sec, the angular speed of the ball is 9.7
rad/s. Determine the magnitudes of the ball’s tangential, centripetal, and...
Simple question: Is there a reason behind the right hand grip rule, or is it just like that (inexplicable)? How do we know that for an object with counter-clockwise rotation (e.g. on the table), the angular velocity is upwards?
Homework Statement
Given a bicycle that is moving at a constant speed of 15.6 m/s with a wheel radius of .32 m...
A. How long will it take the wheel to rotate 19 times?
B. What angle in radians will the wheel rotate in 2.33 minutes?
Homework Equations
theta=angular velocity*time...
Homework Statement
When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4740 rpm to zero in 3.00 s.
A. What is the angular acceleration of the blade(rev/s^2)? GOT IT
B. What is the distance traveled by a point on the rim of the blade during the...
Homework Statement
The Bohr Atom 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 lowest-energy orbit the distance from the proton to the electron is 5.29 * 10^- 11 m, and the linear speed of the electron...
Homework Statement
Suppose a uniform sphere of mass M and radius R is placed on a rough horizontal surface. It rolls without slipping.
We can apply 2 equations.
1) considering the torque due to frictional force about the centre of mass,
fR=I(alpha)
here alpha=a/R as the it is in pure...
Homework Statement
An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 420 rev/min. If the angular acceleration is constant, how many reovlutions does the propeller undergo during this time?
Homework Equations
\theta = \omega 0 t +1/2 \alpha...
Homework Statement
4. An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s².
a) Compute the angular velocity of the turntable after 0.200s my answer:1.35rev/s...
Homework Statement
A mass (M) is dropped from height (H) onto one end of a stick of mass (M) and of length (L) pivoted around the opposite end. Upon collision the mass adheres to the stick. Respond to the following in terms of M, L, H, and g.
a. Find speed of mass just before impact
b. Find...
Homework Statement
The given information is:
A Ferris wheel with a radius of 9.0 m rotates at a constant rate, completing one revolution every 37 s.
Suppose the Ferris wheel begins to decelerate at the rate of 0.22 rad/s^2 when the passenger is at the top of the wheel.
(1) Find the...
Homework Statement
http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam3/fa07/fig19.gif
A dumbbell consists of a slender rod of negligible mass and length L = 1 m and small steel balls attached to each end with mass 1 kg and 2 kg, respectively. It...
Homework Statement
http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam3/sp08/fig23.gif
A child sends a hula hoop (moment of inertia I = MR^2) sliding without rolling across a smooth floor. The hoop has an initial velocity Vsliding. The hoop...
Homework Statement
A woman whose mass is 70 kg stands at the rim of a horizontal turntable that has a moment of inertia 300 kg m^2 and radius of 2 m. The system is initially at rest and is free to rotate about frictionless vertical axle through the center of the turntable. The woman begins to...
Homework Statement
http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam3/fa08/fig10.gif
A spool of mass M = 1 kg sits on a frictionless horizontal surface. A thread wound around the spool is pulled with a force T = 4 N as shown below. The total...
Homework Statement
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/spring09/homework/10/bowling_ball/8.gif
A bowling ball 25 cm in diameter is slid down an alley with which it has a coefficient of sliding friction of µ = 0.6. The ball has an initial...
Homework Statement
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/spring09/homework/10/three_cylinders/6.gif
Three identical, solid, uniform density cylinders, each of mass 17 kg and radius 1.67 m, are mounted on frictionless axles that are attached to...
Homework Statement
A 1 kg ball is traveling horizontally at 10 m/s. It hits a stick of mass 1kg and length 1.2m (rotational inertia 1/12 M L^2) at the bottom of the stick, which rotates upward 90 degrees from its previous location. The ball's direction changes by an angle theta. Find theta and...
Homework Statement
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/spring09/homework/09/pivoting_stick/5.gif
A stick of uniform density with mass M = 8.7 kg and length L = 0.6 m is pivoted about an axle which is perpendicular to its length and located...
Homework Statement
The wheel of fortune wheel, whose radius is 3.00m, has 20 different numbers, at equal intervals, for a contestant to land on. The second contestant can spin the wheel, and wishes to land on the $1.00. The wheel starts off 4 positions away from the $1.00. Assuming a...
Homework Statement
A hollow cylinder of length L and radius R has a weight W. Two cords are wrapped in the same direction around the cylinder, one near each end. The cords are fixed to the ceiling. The cylinder is held horizontally with the cords vertical. The cylinder is then released. Find...
Homework Statement
i've altered this image to be easier to read. ignore problem 1 except for the information given. the picture of the rotating object is for problem 2, which is the problem i need help with
http://img32.imageshack.us/img32/3690/screenshot20091121at931x.th.png
2. The attempt...
Note - pi is not meant to be an exponent, not sure why it looks like one...
Homework Statement
The differential gear of a car axle allows the wheel on the left side of a car to rotate at a different angular speed than the wheel on the right side. A car is driving at a constant speed...
NOTE: In playing with the symbols it appears that I've made pi to be an exponent...um...so anytime you see that, please disregard it as pi is not meant to be an exponent anywhere here. Thanks!
Homework Statement
A gymnast is performing a floor routine. In a tumbling run she spins...
A solid ball with a diameter of 22 cm rolls along a horizontal surface as shown without slipping at a constant acceleration. It initially (t=0) has an angular velocity of 11 rad/s and 10 seconds later has an angular velocity of 3 rad/s.
(a)What is its angular acceleration? rad/s2
(b)What is...
How far has the disk moved?
Disk has .34m radius with a mass of 7.4. The angular acceleration about the center of mass is 100.2 rad/s2.
So this is what i did:
ang. disp= .5(ang. accel)*t^2
(x=.5(a)t^2 =>pretty much)
I got my ang. disp to be 84.669 rad. Now i need to convert it to meters.
The...
Homework Statement
If you step on your car's brakes hard, the wheels stop turning (i.e., the wheels "lock") after 2.0 revolution.
Part A.
At the same constant acceleration, how many revolutions do the wheels make before stopping if your initial speed is twice as high?
Homework...
Homework Statement
A thin rod (length = 1.50 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod. The rod, starting from rest, tips over and...
Homework Statement
Problem statement: Please see the attached picture. A rigid rod rotates with constant angular velocity w. A rigid bar with length A is attached perpendicular to the rotating rod. A second rigid bar with length B is attached to the other end of bar A by a hinge. The...
Homework Statement
The drive propeller of a ship starts from rest and accelerates at 2.90e-3 rad/s^2 for 2.1e3 seconds. For the nest 1.4e3 seconds, the propeller rotates at a constant angular speed. Then it decelerates at 2.3e-3 rad/s^2 until it slow (without reversing direction) to an...
Homework Statement
A ball at the end of a string of length 0.75 m rotates at a constant speed in a horizontal circle. It make 3 rev/s.
What is the period of the ball's motion?
What is the ball's angular velocity?
Homework Equations
w = delta theta/delta t
theta = 2*pi*r/r =...
I was just wondering where this comes from. Our professor was giving a lesson on the simple pendulum in the lab class. I copied all of the equations and how he manipulated then I understood, except for this part. I forgot to ask after class, but if you can explain it or want more relative...
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 4.2 m down a q = 26° incline. The sphere has a mass M = 5.1 kg and a radius R = 0.28 m.
a) Of the total kinetic energy of the sphere, what fraction is translational?
b) Suppose now that there...
Homework Statement
A circular hoop rolls down a ramp without slipping. The angle of the ramp with respect to horizontal is 30 degrees.
1) What is the acceleration of the center of mass of the hoop down the ramp?
a = ( 1/4 ) g
a = ( 1/3 ) g
a = ( 1/2 ) g
a = ( 2/3...
Homework Statement
If the melting of the polar ice caps were to raise the water level on the Earth by 10m, by how much would the say be lengthened? Assume the moment of inertia of the ice in the polar ices caps in negligible (they are very near the axis), and assume that the extra water...
When it is 10:00, the hour hand on an analog clock is 300 ahead of the minute hand. How many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand?
I seems really easy, but for some reason I am not getting the right answer...
Three identical, solid, uniform density cylinders, each of mass 16 kg and radius 1 m, are mounted on frictionless axles that are attached to brackets of negligible mass. A string connects the brackets of cylinders #1 and #3 and passes without slipping over cylinder #2, whose bracket is attached...
http://img267.imageshack.us/img267/9499/diskwithblockpu2.gif
A uniform disk of mass Mdisk = 4.9 kg and radius R = 0.26 m has a small block of mass mblock = 2.6 kg on its rim. The disk rotates about an axis a distance d = 0.15 m from its center that intersects the disk along the radius on...
Homework Statement
A block of mass m1 = 2 kg rests on a table with which it has a coefficient of friction µ = 0.53. A string attached to the block passes over a pulley to a block of mass m3 = 4 kg. The pulley is a uniform disk of mass m2 = 0.4 kg and radius 15 cm. As the mass m3 falls, the...
Homework Statement
a) A 1.79 kg toy train accelerates constantly from 0.82 m/s to 3.43 m/s in 0.479 revolutions while traveling around a circular track of r 16.7 cm. Find:
- α, magnitude of the angular acceleration.Homework Equations
The Attempt at a Solution
I first tried getting...
Homework Statement
A certain non-uniform but cylindrically symmetric cylinder has mass 9 kg, radius 1.2 m, and moment of inertia about the center of mass 7.6 kg m2. It rolls without slipping down a rough 20° incline.
What is the acceleration of the cylinder's center-of-mass...
Gyroscope-- Angular Speed, Rotational Kinematics, Precession
Homework Statement
A Gyro Stabilizer. The stabilizing gyroscope of a ship is a solid disk with a mass of 6.50×10^4 kg; its radius is 2.30m, and it rotates about a vertical axis with an angular speed of 500 rev/min.
1) How much...
A coin with a diameter of 1.50 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 13.4 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 2.03 rad/s2, how far does the coin roll...
1. A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.00rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0rad/s. While this change...
The question and solution is here
http://i359.photobucket.com/albums/oo31/tanzl/Set4Problem3.jpg
The solution is quite long. Is there any way I can use conservation of momentum (translational or rotation) to calculate this question? such as
initial momentum of ball = final momentum of...
Rotational Kinematics HELP!?
I desperately need help with two rotational kinematics problems. I do not know what to do in both cases. If someone could be kind enough to go through a solution for me to see it would be very helpful in understanding the problem. Please try and be detailed in your...
Rotational Kinematics, Challenge!
Homework Statement
A satellite follows an elliptical orbit. The only force on the satellite is the gravity atraction from the planet. The satellites speed at point A is 8000m/s, and it is 6000km away, Point B is 24000km east of the planet, and Point C is...
[SOLVED] rotational kinematics and energy
Homework Statement
A 190 kg woman stands at the rim of a horizontal turntable with a moment of inertia of 1.3x10^3 kg.m^2 and a radius of 0.68 m. The system is initially at rest and the turntable is free to rotate about a frictionless vertical axle...
[SOLVED] Rotational Kinematics
Homework Statement
A person is riding a bicycle, and its wheels have an angular velocity of +18.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is +13.5 revolutions.
(a)...
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...