Physics 2015: Rolling Motion and Moment of Inertia

Purpose

Investigate which factors affect moments of inertia (such as length, mass, and shape).

Calculate moments of inertia for various shapes to check our results.

Physics 2015: Rolling Motion and Moment of Inertia

Equipment

Inclined board on which you can place round objects at the top of the board and let them accelerate towards the bottom:

Physics 2015: Rolling Motion and Moment of Inertia

Activity I: Data Collection

Note that for constant acceleration (like in out setup today) the

velocity increases linearly with time. Therefore,

where

To measure vaverage, all you need is a stopwatch (time t) and a ruler (distance d).

By the way, the acceleration is

t

dvavg averagefinal vv 2

2

22

t

d

t

v

t

va averagefinal

Physics 2015: Rolling Motion and Moment of Inertia

Activity II: Calculating Moments of Inertia

Simply use conservation of energy, which we quickly see from the figure below is

Since we can’t measure w, we use the fact thatto see that

h

22

2

1

2

1 Imvmgh f

r

v f2

2

2

1

2

1

r

vImvmgh f

f

Physics 2015: Rolling Motion and Moment of Inertia

With this equation we can solve for I, which is the moment of inertia of the rolling object and calculate I from the measured data.

For many round objects I can be calculated as I = Kmr2, where r is the radius, m is the mass, and K is a number dependent on the mass distribution and shape.

To compare your results to theory, write I as I = Kmr2 in the equation above and then solve the equation for K. Then you will have an expression for K as a

function of g, h, and vf.

Use this formula to calculate K for three different objects from your measured data.

Compare your experimental K-values to those in the literature. (e.g., for a disk K=1/2 as we saw in the “Rotational Motion” lab” last week).

2

2

2

1

2

1

r

vImvmgh f

f