**Chapter 12 Practice 2**

Energy

Moments of Inertia

A 1.5 m rod with a mass of 300 g is able to hinge on one end. It is initially horizontal, but is able to pivot until the rod is vertical, stopping as it hits a barrier. How fast is the tip of the rod moving when it hits the barrier?

6.64 m/s

**A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for**

a. Rotations on its hinges and

b. rotation about a vertical axis inside the door, 15 cm from one edge?

a. Rotations on its hinges and

b. rotation about a vertical axis inside the door, 15 cm from one edge?

**6.9 kg m^2**

**4.05 kg m^2**

A thin, 60.0 g disk with a diameter of 8.00 cm rotates about an axis through its center with 0.300 J of kinetic energy. What is the speed of a point on the rim?

4.47 m/s

The three 240 g masses in the figure are connected by massless, rigid rods. What is the triangle’s moment of inertia about the axis through the center?

What is the triangle’s kinetic energy if it rotates about the axis at 5.0 rev/s ?

19 J

.038 kg m

What would be the moment of inertia if the the axis was through one of the masses?

And its kinetic energy keeping the same rotation rate?

38 J

.0768 kg m

2

2

Parallel axis theorem

A 14-cm-diameter CD has a mass of 21 g . What is the moment of inertia of this disc through the center perpendicular to the face of the disc?

What about through an axis at the edge perpendicular to the face of the disc?

5.1 x 10 kg m

1.5 x 10 kg m

-5

2

2

-4

How much further up a ramp will a hoop go than a solid disk, if they start out at the same initial velocity?

33% further

In the figure, a very light rope is wrapped around a wheel of radius R = 2.0 meters and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel?

54 kg m

2

A 350 g ball and a 540 g ball are connected by a 48.0-cm-long massless, rigid rod. The structure rotates about its center of mass at 170 rpm. What is its' rotational kinetic energy?

7.75 J

"What variables does kinetic energy depend on?

"How does the parallel axis theorem work? How does it relate to the center of mass?"

I know you have explained it a billion times but how do we calculate the moment of inertia?