The particles as shown in the figure below are connected by a very light rod. Th

ID: 2013398 • Letter: T

Question

The particles as shown in the figure below are connected by a very light rod. They rotate about the y axis at 1.7 rad/s.

(a) Find the speed of each particle, and use it to calculate the kinetic energy of this system directly from 1/2mivi^2 .

speed of m1 = 1 kg m/s

speed of m2 = 3 kg m/s

speed of m3 = 3 kg m/s

speed of m4 = 1 kg m/s

kinetic energy= J

(b) Find the moment of inertia about the y axis, calculate the kinetic energy from K = 1/2I2.

moment of inertia kg·m2

kinetic energy J

( a )

v = r ;

for m1 , v = 1.7 * 0.4 = 0.68 m / s;

m2 , v = 0.34 m /s ;

m3 , v = 1.7 * 0.2 = 0.34 m /s ;

for m4 , v = 1.7 * 0.4 = 0.68 m / s ;

K = 0.5 [ m1 v1^2 + m2 v2^2 + m3 v3^2 + m4 v4^2 ] ;;

K = 0.5 [ 1 * 0.68^2 + 3 * 0.34^2 + 3 * 0.34^2 + 1 * 0.68^2 ]

K = 0.8092 J <---------ans

( b )

I = m1 r1^2 + m2 r2^2 + m3 r3^2 + m4 r4 ^2

I = 1 * 0.4^2 + 3 * 0.2^2 + 3 * 0.2^2+ 1 * 0.4^2 ;

I = 0.56 ;

K = 1/2 I ^2 ;

K = 0.5 * 0.56 * 1.7^2 ;

K = 0.8092 J <----------ans

( c )

the results obtained are one and the same only

K from ( a ) = 0.8092 J ;

K from ( b) = 0.8092 J ;

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