3, A toy top consists of a rod, which has negligible mass and diameter d 0.5 cm,

Question

3, A toy top consists of a rod, which has negligible mass and diameter d 0.5 cm, attached to the base of a solid uniform density circular cone of radius r height h = 2 cm, and mass m = 10 g. 1 cm, cIn a. Calculate the moment of inertia of the top rotating about its center axis. (do not just look it up!) Hint: consider integrating the moment of inertia of a solid disk. b. A length L 10 cm of string is tightly wrapped around the rod, thern 1 N. After the pulled off (without slipping) with a constant tension T string is pulled off, how fast is the top rotating?

Explanation / Answer

a)

ITop = Irod + Icone = 0 + (3/10)mR^2 = 0.3*10*0.01^2 = 0.0003 kg*m^2

b)

Torque = I

F*r = I --------------(1)

By kinematic eqn,

wf^2=wi^2+2*

At initial wi= 0rad/s

wf^2=0^2+2*

=wf^2/(2)---------------(2)

linear distance=d=r*

=d/r = 0.10m/0.005m = 20 rad --------------(3)

From (1), (2) and (3)

F*r = I*[wf^2/(2*20)]

1.0*0.005 = 0.0003*[wf^2/(2*20)]

wf= 25.82 rad/s

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