# Physics 2011 Lab 9 Momentum of Inertial

Physics 2011 Lab 9Momentum of Inertia, /Formal Lab Report/

Object: To measure the momentum of inertia of rigid body and to compare with that of the theoretical models.

Apparatus:

- iMac and ScienceWorkshop interface;
- Smart-pulley System.

Theory: The angular acceleration of a rigid body is proportional to the net torque applied to the rigid body,

τ = I α

where α is the angular acceleration, τ is the net torque and I is the momentum of inertia of the rigid body. From Newton’s laws, we can derive that

where r is the distance between dm to the rotational axis. For a disk rotating around the center symmetric axis, its momentum of inertia is

where R is the radius of the disk. For a ring rotating around the center symmetric axis, its momentum of inertia is

where RInner and ROuter are its inner and outer radius respectively. For a rectangular bar rotating around 2-fold symmetric axis in the thickness direction, its momentum of inertia is

where L and B are its length and width respectively

Procedure:

- Turn on iMac computer
- Turn on Scienceworkshop interface
- Open DataStudio™ and choose the smart pulley experiment.
- Click on the graph icon to open the monitoring windows
- Set up the Smart Pulley system. Add 100g masses to the hanger. Hold on the pulley system to rest.
- Release the smart pulley system. At the same time, click the start button to record the acceleration of the hanger. Click the stop button before the disk start to rewind.
- Click the Fitting button and select linear fitting. Record the slope as the acceleration of the hanger. The angular acceleration of the disk system is then

where α is the angular acceleration, r is the radius of the pulley attached to rotation disk and a is the acceleration of the hanger.

- Repeat step 5-7 according to the following setups.
- Disk only
- Disk + Ring
- Disk + Bar

Results

* I = τ /α

** τhager=r*F = r * (Mhanger*(g-a)) ~ Mhanger*g*r

Table I: Diskr =

Disk: MDisk=, R =

Trial Mhangerτhangera αIDisk

1

2

3

4

5

Average IDisk = Standard deviation =

Table II: Disk + Ringr =

Ring: Mring=,RInner=ROuter=

Trial Mhangerτhangera αIDisk+RingIRing = (Idisk+ring-Idisk)

1

2

3

4

5

Average IRing = Standard deviation =

Calcuated:

Error percentage:

Table III: Disk + Barr =

Ring: MBar=,L=B=

Trial Mhangerτhangera αIDisk+BartIBar = (IDisk+Bar-IDisk)

1

2

3

4

5

Average IBar = Standard deviation =

Calculated;

Error percentage: