[satterly] the pendulum 31 



t = 1% 



V 



g 

 L= ^ 



Numerically, in the case considered 

 32-2 X 3-762 



= 11-50 feet 



4 X 9-87 



Measure the diameter of the sphere with the block of wood F, 

 get the radius and the length of the hook and subtract from the above 

 to get 1, the length of the wire. 



The diameter = 6 - 25 inches = -52 feet 



The radius = - 26 feet 



The length of the hook= 1-9 inches = - 16 feet 



Therefore, length of wire = 11 -50- (26+ • 16) = 11 -04 ft. 



If the length of the psndulum had been known the experiment 

 could have been treated as an exercise on the Triangle of Forces, 

 and the weight of the ball deduced. 



Experiment V. — The Modulus of the Rigidity of the Suspension 

 Wire. — ^Set the ball vibrating around the wire as axis and take its 

 period of vibration. To facilitate this, a vertical white line is painted 

 on the ball (see photograph). The vibrations should be timed in 

 successive fives as described above. 



The time of vibration is given by the formula 



^ = 27r Moment of Inertia of the Ball about vertical axis 



^ Couple of restitution exerted by the wire per unit angular 

 ^ displacement. 



If 1 =the length of the wire in feet 



a = radius of cross section of wire, in feet 



n = modulus of rigidity of material of wire 



I = Moment of inertia of ball about the axis of vibration 



2k 



4 



ti^a* 



21 



2 Mr 



In the case of a suspended sphere I 



where M = mass of sphere r = radius of sphere 



16 TtUrH 



5 ti2 a 



2 a4 



I L i ki K ,^ Î? Y 1 : 



