MC-9a: Angular Acc. & Moments of Inertia Name______

Modified Lab Worksheet: Group member names______

This sheet is the lab document your TA will use to score your lab. It is to be turned in at the end of lab.

1. Set up the rotational inertia apparatus according to the Experiment I section of the lab manual following steps 1 through 4.

Draw a free body diagram for just the hanging mass in terms of its mass m, the acceleration of gravity g and the string tension T. / Using Newton's 2nd Law, solve forT in terms of ay (the acceleration of the hanger), m and g.
Using a top view perspective, draw a FBD for the heavy gray disk in terms of the hub radius r and string T. For rotational motion you must keep the forces in their respective positions. / Newton's 2nd Law for rotational motion relatesthe tension T in term of z (the angular acceleration of the disk), in terms of r, M and R.
rT=(½MR2)z
Here ½MR2is the inertia (I) to rotational motion for a solid cylinder if the axis of rotation is perpendicular to the plane of the disk and passes through the center of the disk.
  1. If the grey disk rotates exactly one full revolution then how much does the hanging mass displace? y: ______±______
  2. If the grey disk rotates exactly five full revolutions then how much does the hanging mass displace? y:______±______
  3. Are the results of 2 & 3 consistent? ______
  4. Measure these quantities and estimate the error:

Mass of gray disk, M: ______±______

Radius of gray disk, R:______±______

Rotational inertia of gray disk, I = ______

Radius of middle hub, r:______±______

  1. Does y=2 r? Does the string’s radius have an effect?

______

  1. How are ay and z related?______
  2. Eliminating T and ay , weobtain an expression that relates zto r, M, g and R.

z = (mgr)/( ½ MR2+ m r2 )

  1. Use these numbers and a value of m = 100 g and g = ______to obtain

your “expected” values for z =______and ay =______

(a value of ay = 0.015 m/s2 is typical)

  1. Now following the lab manual procedure (steps 5 through 7) and measure ay three times.
  2. Measurements of ay :

Mean value of ay =______

  1. How well do your values compare?______
  2. Perhaps you will do better if you eliminate two systematic errors, frictional forces and the effective hub radius (i.e., the string itself has a finite radius and so if may be expected that your hub radius, r, value is small than the actual value).
  3. Measure m0, the mass necessary to balance the frictional forces and the effective hub radius following step 9 in the manual.

m0:______±______

# revolutions:______±______

h1:______±______

h2:______±______

r':______±______

Using m0 and r' obtain your “corrected” values for z =______and ay =______

  1. How well do these values compare?______

Mean value of ay =______

Work-Energy: You could have used the Conservation of Energy principle directly. If your system was said to by the hanging mass and the gray disk, ignoring friction, then the mechanic energy would be constant:

Emechanical = Etranslational + Krotational + Ugravitational= ½ mvy2 + ½ I 2 + mgy

Where vy = r

(Before) 0 + 0 + mgh1: = ½mvy2 + ½ ( ½ MR2 ) (vy/r)2 + mgh2 (After)

  1. Arrange for 150 grams to descend a distance of 60 to 70 cm and record the maximum velocity when starting from rest.

h1:______±______

h2:______±______

h:______

Using the above energy expression now calculate the expectedvy :______

Run the same experiment and measure vy :

Mean value of vy =______

  1. How much rotational energy does the gray disk have?

Krotational=______

  1. How much translational kinetic energy does the falling mass have?

Ktranslational=______

  1. Now remount the gray disk so that it stands on end and rerun the experiment over the same y displacement.

New value of vy =______

  1. Has vy increased or decreased?______
  2. Has ay increased or decreased?______
  3. Can you suggest a reason why these values are different?______

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