13. Rotational Inertia & Energy

Intro to Moment of Inertia

Open Question
Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. (a) A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular to it and passing through (i) one end and (ii) its center, and (iii) about an axis parallel to the rod and passing through it.
Multiple Choice
A system is made of two small masses (M_LEFT = 3 kg, M_RIGHT = 4 kg) attached to the ends of a 5 kg, 2-m long thin rod, as shown. Calculate the moment of inertia of the system if it spins about a perpendicular axis through the mass on the left.
Multiple Choice
A solid disc 4 m in diameter has a moment of inertia equal to 30 kg m² about an axis through the disc, perpendicular to its face. The disc spins at a constant 120 RPM. Calculate the mass of the disc.
Multiple Choice
A mechanic gives a bicycle tire a spin causing it to rotate at 2.3 rpm. If the mechanic was pushing for $0.5 s$ , what was the average angular acceleration of the wheel while it was speeding up.
Multiple Choice
The figure shows all the forces acting on a $2.0 kg$ solid disk of diameter $4.0 cm$ . What is the magnitude of the disk's angular acceleration?
Open Question
CALC A slender rod with length L has a mass per unit length that varies with distance from the left end, where x = 0, according to dm/dx = gx, where g has units of kg/m^2. (b) Use Eq. (9.20) to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Use the expression you derived in part (a) to express I in terms of M and L. How does your result compare to that for a uniform rod? Explain.
Open Question
You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.400 kg. (a) What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod?
Open Question
If we multiply all the design dimensions of an object by a scaling factor f, its volume and mass will be multiplied by f^3. (a) By what factor will its moment of inertia be multiplied?
Open Question
An object whose moment of inertia is 4.0 kg m^2 is rotating with angular velocity 0.25 rad/s. It then experiences the torque shown in FIGURE EX12.25. What is the object's angular velocity at t = 3.0s?
Open Question
The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods. (b) Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page.
Open Question
The three 200 g masses in FIGURE EX12.11 are connected by massless, rigid rods. (b) What is the triangle's kinetic energy if it rotates about the axis at 5.0 rev/s?
Open Question
The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. (b) Find the moment of inertia about a diagonal axis that passes through masses B and D.
Open Question
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ = cx^2 , where x is measured from the center of the rod and c is a constant.c. Find an expression in terms of L and M for the moment of inertia of the rod for rotation about an axis through the center.
Open Question
A 70.0-kg person stands on a tiny rotating platform with arms outstretched.

(a) Estimate the moment of inertia of the person using the following approximations: the body (including head and legs) is a 62.0-kg cylinder, 16 cm in radius and 1.70 m high; and each arm is a 4.0-kg thin rod, 60.0 cm long, attached to the cylinder.