Question

A 30 kg mass and a 20 kg mass are joined by a light rigid rod and this system is free to rotate in the plane of the page about axis through A and perpendicular to the page. The 30 kg mass is 0.2 m from A and the 20-kg mass is 0.4 m from A. Treating the masses as point masses and assuming the system rotates at 5 rad/s about A, what is the total kinetic energy?

Answer 1

K = 55 J

Step-by-step explanation:

Kinetic energy is a scalar therefore it is an additive quantity

K = ½ I₁ w₁² + ½ I₂ w₂²

The moment of inertia of a particular is

I = m r²

I₁ = 30 0.2² = 1.2 kg m²

I₂ = 20 0.4² = 3.2 kg m²

As the body is joined by a rigid rod they both have the same angular velocity

K = ½ (I₁ + I₂) w²

Let's calculate

K = ½ (1.2 + 3.2) 5²

K = 55 J

Answer 2

55 J

Step-by-step explanation:

Kinetic energy is given as: 0.5MV^2 where M is the mass and V is the speed of rotation. Since the masses are point masses, we calculate the point mass for each mass.

M1 = 30*0.2^2 = 1.2kgm^2

M2 = 20*0.4^2 = 3.2kgm^2

V = 5 rad/s

Calculating using the formula above, we obtain :

0.5(1.2+3.2)5^2 =0.5*4.4*25 = 55 J