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 1.10 rad/s. Find the total rotational kinetic energy evaluated from 1/2 Iomega ^2. How is the variable omega in the equation for the kinetic energy related to the angular speed? Find the tangential speed of each particle. 4.00 kg particle 2.00 kg particle 3.00 kg particle 4.2 What is the equation relating the angular speed to the tangential speed? m/s Find the total kinetic energy evaluated from sigma 1/2 m_1v_1^2.

Explanation / Answer

given that

m1 = 4 kg

m2 = 2 kg

m3 = 3 kg

r1 = 3 m

r2 = 2 m

r3 = 4 m

w = 1.10 rad/s

(a)

moment of inertia about x axis

I = I1+I2+I3

I = 4kg * (3m)^2 + 2kg * (2m)^2 + 3kg * (4m)^2

I = 92 kg*m^2

(b)

rotational kinetic energy KEr = 1/2*I*w2

KE = 1/2*92*(1.10)^2

KE = 55.66 J

(c)

we know that

v = w*r

speed of 4kg particle

v1 = 1.10*3 = 3.3 m/s

speed of 2kg particle

v2 = 1.10*2 = 2.2 m/s

speed of 3kg particle

v3 = 1.10*4 = 4.4 m/s

(d)

total kinetic energy

KE = KE1+KE2+KE3

KE = 1/2[(4*(3.3)^2) +(2*(2.2)^2) + 3*(4.4)^2)]

KE = 55.66 J

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