We are going to start out this lab by investigating how to calculate the moment

Question

We are going to start out this lab by investigating how to calculate the moment of inertia. Let's start out by considering the barbell shown in Figure P-1. 'Moment of Inertia' is the measure of an object 's resistance to rotational motion, also known as its 'rotational inertia'. Shown here are two barbells. They have the same mass but have different moments of inertia. Each is intended to be held in the center and twisted. The bars shown Figure P-1 have two different configurations. Use the in information given in the moment of inertia facts to determine an equation for the moment of inertia for each of the two configurations. Assuming that a person's hand is placed in the center twists bar. a) Masses Close: b) Masses Far Which one would you expect to have a larger moment of inertia? Moment of Inertia Facts The moment of inertia of the pipe rotated about its center of mass. I = 1/12 ML^2 M is the mass of the pipe and L is the overall length of the pipe. The moment of inertia of an object rotating about an exterior point is I = MR^2, M is the mass and R is the distance from the center of the object to the center of rotation. The moment of inertia of a system of objects is the sum of the moments of inertia of the objects that make up that system.

Explanation / Answer

masses Far

moment of inertia of the system = moment of inertia of the bar + moment of inertia of the two masses

I = I_bar + I_mass = (1/12)*M*L^2 + (2*m*R^2)

R = L/2

M is the mass of the bar and m is the mass of the two objects

then I = (1/12)*M*L^2 + (2*m*(L/2)^2) = (1/12)*M*L^2 + (m*L^2/2) = [(M/12)+(m/2)]*L^2

masses close

I = 1/12)*M*L^2 + (2*m*R^2)

this time R is smaller than R in the first case,hence

the moment of inertia in case of masses far is larger than masses close

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