Activity 7 Inertial Balance Part 2

OBJECTIVE: To feel how inertia effects acceleration. BACKGROUND: The inertial balance in Part 1 of this activity operates by virtue of the fundamental property of all matter that causes it to resist changes in motion. In the case of the inertial balance, the resistance to motion is referred to as rotational inertia. This is because the yardstick pivots at the point on the table where it is anchored and the bucket swings through an arc. Unlike linear motion, the placement of mass in rotational movements is important. Rotational inertia increases with increasing distance from the axis of rotation.

The inertial balance in Part 1 uses a metal yardstick as a spring. The bucket for holding samples is located at the end opposite the axis of rotation. Moving the bucket closer to the axis will make a stiffer spring that increases the sensitivity of the device.

The relationship of the placement of mass to distance from the axis of rotation is easily demonstrated with a set of inertia rods. The rods are identical in appearance and mass and even have identical centers of mass. Yet, one rod is easy to rotate and the other is difficult. The secret of the rods is the location of the mass inside of them. In one rod, the mass is close to the axis of rotation, and in the other, the mass is concentrated at the ends of the rod. Students will be able to feel the difference in rotational inertia between the two rods as they try to rotate them.

MATERIALS NEEDED: PVC 3/4 in. water pipe    (about 1.5 to 2 m long) 4 iron pipe nipples    (sized to fit inside PVC pipe) 4 PVC caps to fit water pipe Silicone rubber sealant Scale or beam balance Saw Very fine sand paper 1/2 in. dowel rod   PROCEDURE: Step 1. Using a saw, cut the PVC tube in half. Smooth out the ends, and check to see that the caps fit the ends. Step 2. Squeeze a generous amount of silicone rubber sealant into the end of one of the tubes. Slide the nipple into the tube. Using the dowel rod, push the nipple to the middle of the tube. Add sealant to the other end of the tube and insert the second nipple. Position both nipples so that they are touching each other and straddling the center of the tube. Set the tube aside to dry. Step 3. Squeeze some sealant into the ends of the second tube. Push the remaining pipe nipples into the ends of the tubes until the ends of the nipples are flush with the tube ends. Be sure there is enough compound to cement the nipples in place. Set the tube aside to dry.

Step 4. When the sealant of both tubes is dry, check to see that the nipples are firmly cemented in place. If not, add additional sealant to complete the cementing. Weigh both rods. If one rod is lighter than the other, add small amounts of sealant to both ends of the rod. Re-weigh. Add more sealant if necessary. Step 5. Spread some sealant on the inside of the PVC caps. Slide them onto the ends of the tubes to cement them in place. Step 6. Use fine sand paper to clean the rods.

QUESTIONS: How does the placement of mass in the two rods affect the ease with which they are rotated from side to side? Why? If an equal side to side rotational force (known as torque) was exerted on the middle of each rod, which one would accelerate faster?