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A cylinder rolls without slipping over a horizontal plane. The radius of the cylinder is equal to r. Find the curvature radii of trajectories traced out by the points A and B(see figure) |
Answer» Solution :Let US DRAW the kinematic diagram of the rolling cylinder on the basis of the solution of PROBLEM 1.53.   As, an arbitrary point of the cylinder follows a curve, its normal acceleration and radius of CURVATURE are related by the well known equation `w_n=v^2/R` so, for point A, `w_(A(n))=(v_A^2)/(R_A)` or, `R_A=(4v_c^2)/(omega_r^2)=4r` (because `v_c=omegar`, for PURE rolling) Similarly for point B, `w_(B(n))=(v_B^2)/(R_B)` `omega^2rcos45^@=((sqrt2v_c)^2)/(R_B)`, `R_B=2sqrt2(v_C^2)/(omega^2r)=2sqrt2r` |
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