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.

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  1. A

    Question on Rotational Dynamics

    1.A uniform Disc of Radius R is rotating in its own plane with angular velocity w when it is placed flat on a rough table. If u the coefficient of sliding friction is independent of velocity show that the time taken for the disc to come to rest is (3RW)/(4ug). How does the kinetic energy of...
  2. P

    More Rotational Dynamics

    Ok I'm in desperate need of some direction! I have the following question in which I must answer twice once using rotational dynamics and then again using Conservation of Mechanical Energy. Question: A massless string is wrapped around a solid cylinder as shown in the diagram at the right...
  3. P

    Rotational Dynamics: Moment of Inertia of 0.44 kg Meter Stick

    Wanted to check this question also: A meter stick of mass 0.44 kg rotates, in the horizontal plane, about a vertical axis passing through the 30 cm mark. What is the moment of inertia of the stick? (Treat it as a long uniform rod) Answer: I = 0.1628 kg.m^2 Correct??
  4. K

    Solving Rotational Dynamics: 4.0 Nm Torque, 4.0 kg Cylinder, 2.0 s

    Hello there, I've got a problem here. A solid cylinder of radius 0.8 m and mass 4.0 kg is at rest. A 4.0 N m torque is applied to the cylinder about an axis through its centre. Calculate the angular velocity of the cylinder, in rad s-1 , after the torque has been applied for 2.0 s. how do...
  5. G

    How Do I Solve These Rotational Dynamics Problems?

    I have a couple questions could someone help? I tried everything and I just don't understand what's going on. Thank you sooo... much! :D 1)A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.0600 m, an angular speed...
  6. J

    Problems w/ rotational dynamics and angular momentum

    1) A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.20 m-N. If the mass of the rotor is 4.8 kg and it can be approximated as a solid cylinder of radius .0710 m, through how many revolutions will the rotor turn before...
  7. N

    Rotational Dynamics - sphere,block,pulley

    :confused: A solid sphere (I=(2/5)MR^2) with a radius R=0.10m is attatched to a massless rope by a frictionless axle that passes through the center of the sphere. The rope passes over an ideal pulley and is connected to a 1kg block. The sphere has a mass of 2kg. The surface has a meu that...
  8. C

    Angular Displacement in Rotational Dynamics

    Why do we use the angle as the base quantity in rotational dynamics instead of, perhaps, arc length? Is it because angular displacement is easier to measure? Would it make any sense to use arc length?
  9. J

    Rotational Dynamics and angle of theta

    I tried to do this problem with related rates and calculus. We have not done physics with calculus, however. The other way I thought about was using the angular velocity of the board when the stick is taken away. I cannot seem to solve it though. A common physics demonstration consists of a...
  10. S

    How Is the Tangential Force Calculated in Rotational Dynamics?

    A rope is wrapped around a wooden sylinder with I=2.9 and radius = 0.25m A 50 kg crate is suspended to the free end of the rope and is pulled upwards with an acceleration of 0.80 m/s*s A crank handle is attached to the axle of the wooden cylinder and when turned rotates about the axle in a...
  11. H

    Rotational Dynamics disk of radius Question

    Please could someone check my answers to the following and advise me on any of the bits I'm stuck on. Thanks ===== Q. A disk of radius a and mass m is suspended at its centre by a vertical torsion wire which exerts a couple \fontsize{5} -c\theta on the disk when it is twisted through an...
  12. S

    Calculating Forces in a Rotational System with a Wrecking Ball and Boom

    A wrecking ball (weight = 5400 N) is supported by a boom, which may be assumed to be uniform and has a weight of 3800 N. As the drawing shows, a support cable runs from the top of the boom to the tractor. The angle between the support cable and the horizontal is 32°, and the angle between the...
  13. C

    Need help on a rotational dynamics problem for tomorow please

    hi i need help understanding what to do with the information that was given in the problem if u could point mein the right direction i would greatly appreciate it. thank you An invered "A" is suspended from the ceiling by 2 verticle ropes. Each leg of the "A" has a length of 2L and a weight...
  14. C

    Need help on rotational dynamics problem quick please

    hi i need help understanding what to do with the information that was given in the problem if u could point mein the right direction i would greatly appreciate it. thank you An invered "A" is suspended from the ceiling by 2 verticle ropes. Each leg of the "A" has a length of 2L and a weight...
  15. E

    Solving Rotational Dynamics Problems with Torques & Acceleration

    Hello, I have a problem dealing with torques and acceleration. I am sure I solved it right but when submitting the answers, I get the response "Incorrect" :cry: The problem: A wheel of radius 2 m, mass 53 kg, and moment of inertia (3/4) (53 kg) (2m)^2 about the center of mass is mounted...
  16. M

    Question on rotational dynamics

    Here is the question (it's part of a lab): "From your lectures in mechanics you should be able to derive: \alpha = \frac{mgr}{I+mr^2} This equation ignores the effect of the pulleys and the mass of the connecting string" The lab was basically setting up a mass on a string over a pulley...
  17. R

    How Far Will a Coin Roll Before Stopping?

    Here's the problem: diameter = 3.45 cm angular speed = 11.4 rad/s angular deceleration = -.96 rad/s How far does the coin roll before coming to a stop? How would I set this problem up? Thanks!
  18. N

    Rotational Dynamics and torque, easy problem

    I really have no idea how to go about doing this one... Any help is well appreciated! Thanks! What is the angular acceleration of the rectangle in (attachment) if a torque of 13 Nm is applied about (a) the x-axis (b) the y-axis and (c) the z axis (through origin and perpendicular to the...
  19. denian

    Rotational Dynamics: Calculations for A-Level Physics

    im doing questions from "Calculations for A-Level Physics" answers not provided for this Q. Question : A grinding wheel of radius 0.080m is driven by an electric motor at a constant speed of 50 rps. A piece of steel is pressed against the outer rim of the wheel, producing tangential force...
  20. R

    Rotational dynamics of platform

    I have no clue on this, I am stumped anyone have an idea. a platform is rotating at an angular speed of 2.2rad/s.A block is resing on this platform at a distance of 0.30m from the axis. The coefficient of static friction between the block and the platform is 0.75. Without any external torque...
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