The cutting arm of the paper cutter is pinned about a fixed axis at O, and its angle relat...

The cutting arm of the paper cutter is pinned about a fixed axis at O, and its angle relative to the horizontal is measured by ϕ. A linear elastic torsional spring at O with constant kt keeps the arm from falling when not in use. Model the cutting arm as a uniform slender bar of length L = 20 in. and weight W = 2.5 lb. Neglect friction in the pin at O.

Determine the angular speed with which the cutting arm will reach the horizontal position ifit is released from rest at ϕi = 70° with kt = 1.6 ft·lb/rad. Assume that the torsional spring is undeformed when ϕ = 90°.

Figure P7.46