In class, we've been working on moment of inertia and recently did a lab regarding its usage. I don't feel too confident with the material yet and was hoping someone could look over my work and offer advice on what to do.
We used solid spheres in the lab (2/5mr^2 used) and measured the height from the object was released, the length of the ramp, radius from the axis of rotation, mass, and time for the object to reach the bottom.
Object 1: h=0.085 m, l=0.7 m, r=0.05 m, m=0.81 kg, t=1.3 s
Object 2: h=0.085 m, l=0.7 m, r=0.025 m, m=0.11 kg, t=1.2 s
Calculations:
1.) Speed of the object at the bottom of the ramp if all it did was slide down (disregard friction).
mgh=1/2mv^2
gh=1/2v^2
v=(2*9.8*0.085)^1/2=1.29 m/s
2.) Speed of the object if it was rotating down the ramp (no slipping).
mgh=1/2mv^2 + 1/2Iω^2
mgh=1/2mv^1 + 1/2(2/5mr^2)(v^2/r^2)
mgh=1/2mv^2 + 1/5mv^2
gh=7/10v^2
v=(10/7*9.8*0.085)^1/2=1.09 m/s
3.) Calculate the angular speed of the object at the bottom of the ramp.
ω=v/r
ω1=1.09/0.05=21.8 rad/s
ω2=1.09/0.025=43.6 rad/s
4.) Assuming no slipping, calculate the number of revolutions it takes for the object to reach the bottom.
Ө=1/2(ωf+ωi)t
Ө1=1/2(21.8+0)(1.3)=14.17 rad=2.26 rev
Ө2=1/2(43.6+0)(1.2)=26.16 rad=4.16 rev
5.) Using #4, calculate Ө (rad).
Ө1=14.17 rad
Ө2= 26.16 rad
6.) Calculate α (rad/s^2).
21.8=0 + 1.3α
α1=16.77 rad/s^2
43.6=0 + 1.2α
α2=36.33 rad/s^2
7.) Calculate t (s).
14.17=0 + 1/2*16.77*t^2
t1=1.3 s
26.16=0 + 1/2*36.33*t^2
t2=1.2 s
However, I know that the time calculated should be different than the time measured and I'm not sure what to do differently...
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