Question 4a A top D 400 cm M 0100 kg A top is made of a di

Question 4a. A top D = 4.00 cm, M = 0.100 kg A top is made of a disk with diameter 4.00 cm and mass 0.100 kg mounted on top a cylindrical base with diameter 1.00 cm and mass 0.150 kg. The top spins without friction on a tiny massless ball at its bottom. A child gets the top to spin by winding a rope around its base and pulling the rope with a constant force of 0.8 N for 0.3 seconds. What is the angular momentum of the top? Enter your answer in kg m2/s ase::1.00cm d 1.00 cm m : : 0.1.50

Solution

Moment of Inertia of the top = M(D/2)^2 + m(d/2)^2 = 0.1*4*10^-4 + 0.15*0.25*10^-4 = 0.4375*10^-4 kg m^2 = I
Radius of base, r = 0.5cm
Force = 0.8N
Torque = 0.8*0.5*`0^-2 = 0.004Nm
Torque = I*(alpha) (alpha = angular acceleration)
alpha = 91.42 rad/s^2

v = u + (alpha)*t
v = 0 + 91.42(0.3) = 27.42 rad/s
angular momentum = I*v = 0.0119 kg rad m^2 per sec