Project ForgeSign up free
Theory of Machines
Kinematics of Mechanisms
GATE 2020
Hard

A circular disk of radius r is confined to roll without slipping between two parallel plates: the top plate moves left with speed v, and the bottom plate moves right with speed 2v (the disk contacts both plates, at P on top and Q on bottom). The magnitude of the angular velocity of the disk is

  • Av/r
  • Bv/2r
  • C2v/3r
  • 3v/2r

Explanation

Let rightward be positive. Contact point P (top, offset +r from center) has velocity −v; contact point Q (bottom, offset −r from center) has velocity +2v. For a rigid body, v_P=v_center−ωr and v_Q=v_center+ωr. Subtracting: v_Q−v_P=2ωr → 2v−(−v)=3v=2ωr → ω=3v/(2r).

Source: GATE ME 2020 Session 2 (ME-2) (2020)

This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.

Start revising free