A disc translates with a velocity of 6v0 at its centre of mass and simultaneously rotates with an angular velocity of 2v0/R. What is the distance of the instantaneous axis of rotation (IAR) from the centre of mass of the disc?

Correct answer: 3R

Solution

The instantaneous axis of rotation is the point with zero velocity. For combined translation and rotation, its distance from the CM satisfies v_cm = omega * d. Thus d = v_cm/omega = 6v0 / (2v0/R) = 3R.

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