The spool of tape shown and its frame assembly are pulledupward at a speed v A =

Question

The spool of tape shown and its frame assembly are pulledupward at a speed vA = 750 mm/s. Knowing that the 80-mmradius spool has an angular velocity of 15 rad/s clockwise and thatat the instant shown the total thickness of the tape on the spoolis 20 mm, determine (a) the instantaneous center of rotation of thespool, (b) the velocities of points B and D. The spool of tape shown and its frame assembly are pulledupward at a speed vA = 750 mm/s. Knowing that the 80-mmradius spool has an angular velocity of 15 rad/s clockwise and thatat the instant shown the total thickness of the tape on the spoolis 20 mm, determine (a) the instantaneous center of rotation of thespool, (b) the velocities of points B and D.

Explanation / Answer

(a)

Va=75mm/s

w=15rad/s

X=Va/w=50mm

CB=20+80-50=50mm

The instantaneous center lies 50mm to the right of the axle

(b)

Vb=(CB)w=(50)(15)=750mm/s

CD=80+50=130mm

Vd=(CD)w=(130)(15)=1950mm/s

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