Rigid rods of negligible mass lying along the y axis connect three particles. Th

Question

Rigid rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular speed of 2.80 rad/s. (The center of mass of mass m1 = 8.20 kg is at location y1 = 6.15 m, the center of mass of m2 = 4.10 kg is at y2 = 4.10 m, and the center of mass of m3 = 6.15 kg is at y3 = 8.20 m.)

(a) Find the moment of inertia about the x axis

(b) Find the total rotational kinetic energy

(c) Find the tangential speed of each particle.

(d) Find the total kinetic energy

Explanation / Answer

total moemnt of inertia is

I = I1 + I2 + I3

= m1r1^2 + m2r2^2 + m3r3^2

= 8.2( 6.15 m)^2 + 4.1(-4.1)^2 +6.15(-8.2)^2

=792.5915 kg m^2

total rotational kinetic energy,

E = 1/2I^2 = 1/2 (792.5915 kg m^2)(2.8)^2

     = 3106.9 J

the tangential speed of each particle,

v1 = y1 w = 17.22 m/s

v2 = y2 w = 11.48 m/s

v3 = yw = 22.96 m/s

(d)

total energy

E = E1 + E2 + E3

= 1/2 m1 v1^2 + 1/2 m2 v2^2 + 1/2 m3 v3^2

= 1215.76644 + 270.17032+1621.02192

=3106.95 J

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.