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Instantaneous centre of rotation

Rigid body dynamics · Physics

Simple pendulum

Interactive 3D

Release the bob and watch true small-angle SHM. The period depends only on the string length.

Controls

Drag the sliders or type a value — the simulation updates live.

m
0.3m2m
°
5°45°

Study notes

Step 1: Consider a wheel of radius 2 m that is rolling forward with a speed of 4 m/s. Pick a point A on the rim at 45° from the vertical. Its linear speed vA is 4 m/s. Step 2: The velocity of point A is tangent to the wheel, so it points horizontally to the right. Step 3: Draw a line perpendicular to this velocity through point A. Step 4: Pick another point B on the rim at 135° (opposite side). Its velocity vB is also 4 m/s but points horizontally to the left. Draw a line perpendicular to vB through B. Step 5: The two perpendicular lines intersect at the centre of the wheel, which is 2 m below the ground. That intersection point is the instantaneous centre of rotation. Since the wheel is rolling without slipping, the ICR is exactly at the point of contact with the ground, which in this case is 2 m below the centre of the wheel.

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