(b) If the pencil rotates without any friction at the pivot point, determine the
ID: 2106330 • Letter: #
Question
(b) If the pencil rotates without any friction at the pivot point, determine the tangential velocity, i.e., Vcir, at the end of the pencil (furthest from the sharp tip of the pencil) just before the pencil impacts on the table. Hint: Notice that the “center of mass†of the pencil is at its center and that the WorkN-C = 0 in this case so that the total mechanical energy of the pencil is conserved
( c) What is the angular acceleration a of the pencil just before impact?
(d) Determine the tangential acceleration at the eraser end of the pencil just before impact. Hint: It is not 9.8m/s2.
Explanation / Answer
a) MOI I = (1/3) m L^2= (1/3) *0.025*10^-2 = 83.333333333e−6 kg m^2............... b) m g L/2 = 0.5 * I W^2 ====> m g L/2 = 1/6 m v^2===. V = sqrt(3 g L ) = 1.7146 m/s c) torque = mg * L/2 ........torque = I alpha .........so alpha = mg L/ (2 I) = 147 rad/s^2........... d) a _tan = L * alpha = 14.7 m/s^2
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