An Elementary Treatise on Precision of Measurement and Laboratory Exercises in Mechanics and Optics

An Elementary Treatise on Precision of Measurement and Laboratory Exercises in Mechanics and Optics

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 edition. Excerpt: ...K' in terms of m, r, and R; and compare this result with that obtained above. To derive an expression for K by calculus' first find an expression for the area da between the dotted circles in Fig. 18; second find an expression for the mass dm of the portion of the ring'or disk which lies between the dotted circles in terms of area do, the area 'rr(R2--r2) of the ring, and the mass M of the ring; third, substitute this expression for dm in d K; and fourth, integrate d K = x2. dm between the limits x= r and x= R. EXPERIMENT 16 MOMENT OF INERTIA OF A BODY BY MEANS OF ' THE BIFILAR PENDULUM Figs. 19 and 20 show a box A and a bar B suspended by two fine wires ww which are l feet long and s feet apart. This arrangement is called a bifilar torsion pendulum. When the suspended body is turned through an angle cents about the central vertical line V in Fig. 20 the two suspending wires exert a (I " recovery torque T on the body, this recovery'" torque is proportional to cents if the angle 1 is small, and the factor k' in the equation T=--k'cents is called the coeflicient of torsional stiflness of the bifilar suspension. Proposition. The value of k' is: where s and l are the distances shown in Fig. 20, m is the mass of the box A and stirrup, M is the mass of bar B, and g is the acceleration of gravity (32.2 feet per second per second or 980 centimeters per second per second). Proof. Imagine the box A to be turned through a very small angle of cents radians about the axis V in Fig. 20. Then the points p and q in Fig. 20 will move towards and away from the reader respectively, and the distance each will move is-5X4, as shown in the diagram DD of Fig. 19, which shows front and back wiresshow more

Product details

  • Paperback | 28 pages
  • 189 x 246 x 2mm | 68g
  • United States
  • English
  • black & white illustrations
  • 1236803973
  • 9781236803979