Question

Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 5.58 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 5.46 kg and r1 = 1.98 m, (2) m2 = 3.64 kg and r2 = 16.50 m, (3) m3 = 3.21 kg and r3 = 3.09 m.
(a) Find the tangential speed of each object.
(b) Determine the total kinetic energy of this system using the expression KE =

Answer 1

Answer:

a) V1=11.05m/s    V2=92.07m/s     V3=17.24m/s

b) KE = 16238.26J

Explanation:

For tangential speeds:

$V1 = \omega*R1=5.58*1.98=11.05m/s$

$V2 = \omega*R2=5.58*16.5=92.07m/s$

$V3 = \omega*R3=5.58*3.09=17.24m/s$

For the kinetic energy, it can be calculated as:

$KE=1/2*\omega^2*(I1+I2+I3)$

Where:

$I1 = m1*R1^2=5.46*1.98^2=21.4kg.m^2$

$I2 = m2*R2^2=3.64*16.5^2=990.99kg.m^2$

$I3 = m3*R3^2=3.21*3.09^2=30.65kg.m^2$

So,

$KE=1/2*5.58^2*(21.4+990.99+30.65)$

KE=16238.26J