BeginnerTopic 35 of 106Engineering Mechanics
Instantaneous centre of rotation
A point with zero velocity at an instant, simplifying planar motion analysis.
In depth
At each instant a body in planar motion appears to rotate about a point of zero velocity, found at the intersection of perpendiculars to velocity directions. Speeds are then v=ω·r from that centre.
Key points
- A rolling wheel has its IC at the contact point
- Move with the body
- Simplifies velocity analysis, not acceleration
ExampleThe top of a rolling wheel moves at 2v relative to the ground.
What is Instantaneous centre of rotation?
A point with zero velocity at an instant, simplifying planar motion analysis.
Why is it important to understand instantaneous centre of rotation?
The instantaneous centre of rotation gives a geometric shortcut to velocities in planar mechanisms, saving a lot of algebra.
Where is the instantaneous centre for a rolling wheel?
At the contact point with the ground, because that point has zero velocity at that instant.
Is the instantaneous centre fixed?
No. It moves as the body moves, so it is valid only for one instant and must be recalculated.
How is Instantaneous centre of rotation used in practice?
Typical applications include finding the velocity of a piston in a linkage at one instant, checking the motion of a wheel rolling on a surface and locating the moving point of a four-bar linkage quickly.
What should I learn before Instantaneous centre of rotation?
Study "Kinematics of rigid bodies" first (topic 34 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Instantaneous centre of rotation?
A rolling wheel has its IC at the contact point. Move with the body. Simplifies velocity analysis, not acceleration.
Can you give an example of Instantaneous centre of rotation?
The top of a rolling wheel moves at 2v relative to the ground.
What comes after Instantaneous centre of rotation?
The next topic is "Rotational dynamics", which builds directly on this one.
How difficult is Instantaneous centre of rotation?
It is classed as Beginner in Engineering Mechanics (topic 35 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.