Dover+Lab+20+-+Rotational+Inertia+Demonstrator

=Experiment #1 Kinematics of Rotational Motion=

Method 1
θ = θ0 + ω0t + .5αt2 α = .3397 rad/sec^2

Method 2
Vertical Displacement = .69 m a = αr a = .0075 m/s^2 Pulley radius = .0225 α = a/r α = .32

.32/.3397 = 94.2% The acceleration values agree within the uncertainty of measurement.

=Experiment #2=

Method 1
Angular acceleration of rotating apparatus = .3397 rad/s^2 Linear Acceleration of falling mass = .0075 m/s^2 Radius of pulley = .0225 Falling mass (m) = .23 kg Ft = (.23)(.0075) = T - (.23)(9.8) Ft = 2.256 I = .0225(2.256)/(.3397) I = .1494 kg * m^2

Method 2
I(pulleys) = .00058 kg m^2 Thin Rods: length = .3625 m, mass = 74.105 kg I (thin rods) = .003246 kg * m^2 (times four) = .012984 kg*m^2 Moveable mass: mass = .184 kg distance from center = .3525 m I (moveable mass) = .02295 (times four) = .091791 kg*m^2 I = .00058 + .012984 + .091791 = .105355 kg*m^2

(.1494 - .105355)/((.1494 + .105355)/2) * 100 = 34.58% Error, so they are not too different

=Experiment #3=

Gravitational Potential Energy
Mass = .230 kg Vertical displacement = 1 m PE = 2.254 J

Translational Kinetic Energy
t (average) = 14.5 sec v (average) = .06897 m/s v (final) = .1379 m/s KE = .02188 J

Rotational Kinetic Energy
Radius of pulley = .0225 m w (final) = 6.1289 rad/s I = .105355 kg*m^2 KE = 1.9788 J

KE (total) = .002188 + 1.9788 = 1.981 J Error = 12.896% The main reason for the difference is friction and human error (not percise measurement).