A spool whose inner core has a radius of 1.00 cm and whose end caps have a radiu

Question

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the top of the core with a constant speed of 29.0 cm/s,

(a) What is the speed of the spool's ground-touching point?
(b) What is the angular speed of the spool? (Take the ground point as the instantaneous axis of rotation)
(c) What is the speed of the top point of the spool?
(d) What is the speed of CM of the spool? (e) What is the speed of the spool?

Explanation / Answer

the lenght of the green line = ( 2 r core ) + ( r rim - r core ) L = r core + r rim ; v = ? L ; so the ? about point B is ? = v / L = 0.29 / ( 0.01 + 0.015 ) ? = 11.6 rad /s velocity of com = ? * d ; d = r rim ; velocity of com = 11.6 * 0.015 ; v com = 0.174 m /s

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