# What is center of rotation: Definition and 15 Discussions

The instant center of rotation (also, instantaneous velocity center, instantaneous center, or instant center) is the point fixed to a body undergoing planar movement that has zero velocity at a particular instant of time. At this instant, the velocity vectors of the other points in the body generate a circular field around this point which is identical to what is generated by a pure rotation.
Planar movement of a body is often described using a plane figure moving in a two-dimensional plane. The instant center is the point in the moving plane around which all other points are rotating at a specific instant of time.
The continuous movement of a plane has an instant center for every value of the time parameter. This generates a curve called the moving centrode. The points in the fixed plane corresponding to these instant centers form the fixed centrode.
The generalization of this concept to 3-dimensional space is that of a twist around a screw. The screw has an axis which is a line in 3D space (not necessarily through the origin), and the screw also has a finite pitch (a fixed translation along its axis corresponding to a rotation about the screw axis).

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1. ### Calculate center of rotation of monocopter

I want to calculate center of rotation for monocopter, from inertial reference frame,earth. One case when fly in the air in one steady height/place and second case is in free space,then has rocket engine instead fan. I draw forces what I think that must exist. m=2kg Ft(thurst)= 100N ω=500RPM...
2. ### I Question about a Rotating system with mass moving inwards

Dear People, I have a question. I have a rotating tube like a line that has two end and one of them is the center of rotation (like a watch arrow just tube), and inside the tube a mass that is moving towards the center of rotation. So the masses moving along the line aka along the length of the...
3. ### Finding tension as a function of distance from the center of rotation

I'm not too sure how to account for both the mass and the rope at once. I think the following are true for the two individually: For the mass at the end, ## T = m ω^2 L ##, following from ##a = v^2/r##and ##v=ωr##. For the rope, ##dT = ω^2 r dM##, where ##dM = λ dr## and λ is the mass per unit...
4. ### Instantaneous center of rotation

In absence of any other forces, if you push a free object not on the center of mass, during the application of the force (not after) should it only rotate around its instantaneous center of rotation (also called pole or center of oscillation/percussion)? Or it can also be subjected to...
5. ### Instantaneous center of rotation

<Mentor's note: ^Moved from a technical forum and therefore no template.> at the instant shown during deceleration, the velocity of the tire is 40 ft/s to the right and the velocity of point A is 5ft/s to the right. locate the instantenous center of rotation. Can the instantaneous center of...
6. ### Angular momentum and when center of rotation is changed

Hello. The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation. For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at...
7. ### Rigid body with center of rotation other than CoM

Suppose we have a rigid body that rotates around a point P other than its center of mass, with point P being a point of the rigid body. This implies that there are external forces to the rigid body. If the external forces cease to exist(like we have an axis passing through P and we suddenly...
8. ### Instantaneous center of rotation

Homework Statement Where are the instantaneous centers of rotation? Instantaneous center of rotation = 1. Velocity is 0 in this point. 2. This can be also a point where 2 parts "touch" each other and have the same velocity in this point. Homework Equations / The Attempt at a Solution...
9. ### Center of rotation of a free rod

Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM. What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation? If not, are the 3...
10. ### Instantanious center of rotation problems

Homework Statement [PLAIN]http://i61.tinypic.com/10dwmtv. what is the instantaneous center of rotation for the rigid body. OA = 16 AB = 25 AD = 60 BC = 35 ωOA=2s-1 Homework Equations Vb=ωCB*BC The Attempt at a Solution I am assuming the values angles and vectors from red...
11. ### Angular velocity when mass is added at center of rotation

Homework Statement A guy is spinning on a chair with his hands at rest on his lap. As he is spinning, a large mass drops into his hands/lap. Does the guy continue spinning at the same rate, a slower rate, or a faster rate? This video demonstrates what happens when the guy drops mass...
12. ### Instantaneous Center of Rotation for a Differential Drive Robot

Hi, I want to find the instantaneous center of rotation of a differential drive robot. Assuming I know that the robot will travel with a particular linear and angular velocity (v,w) I can use the equations (given here http://rossum.sourceforge.net/papers/CalculationsForRobotics/CirclePath.htm...
13. ### Determining angular velocity radius and velocity of the center of rotation

Hey, I am trying to solve the following problem: va=vr+ ω × rra vb=vr+ ω ×(rra+rab) vc=vr+ ω × (rra+rac) I know the vectors va, vb, vc, rab and rac and I want to know the angular velocity vector, the radius rra and the velocity vr. Physically it means that I know 3 points on a rigid...
14. ### Instantaneous Center of Rotation Help Needed

The figure below shows the piston-cylinder-crank arrangement in an internal combustion engine. When the piston is in the position shown in the figure, it has a downward speed of 900ft/min. I converted the 900ft/min to 180in/sec. I did the whole problem but I realized I used the wrong length...
15. ### Center of Rotation w/ 4 Objects: Finding Tension

If w = 1.0 rad/s 0-----0-----0-----0 lenght 1 = 2 m lenght 2 = 3 m lenght 3 = 4 m each circl is a object weighing 1 kg. find center of rotation and tension in the massless rods getting center of rotation was easy but tension.. well i know if there's 3 objects, to get...