Question

A pendulum consists of a rod of mass 2 kg and length 1.3 m with a solid sphere at one end with mass 0.4 kg and radius 15 cm (see the following figure). If the pendulum is released from rest at an angle of 38°, what is the angular velocity at the lowest point? (Enter the magnitude in rad/s.)

38°

1.3 m, 2 kg

0.4 kg, 15 cm radius

Answer 1

Giren mass of rod mi= 2kg length l = 1.3m man of sphere M₂ = 0.4kg radius r = 15 cm 2015m centre of mass of pendulum = min, fly d2 • 20:37 27 0.4 (1.37 0.15) 2+0.4 = 2.6 + 0.5% 2.4 = 1.325 m d=lte moment of inertia of pandelam I = food fasphere = r + ( 2 m atm, d e = } 20-3)*4 = 0.460259+ 0.47 245) = 1.126664 3.6xió + 0.841 = 1.94126 regar aft 38 songervation of energy PE, IKE, = PE att at lower point might fs = mghat I w (2.4) (9.8) 1.325 carg8'ta = 2.4(9.8) 1.325 +2 1.97166 -24.5572-31.164 + 0,98563 w w = 6.7031 w= 2,589 radſee angular velocite, et lowella pointi