Science Buddies: "Ask an Expert"

If I have a wheel, I know it's mass and diameter and the slope of a hill. Can I calculate the time it will take to get to the bottom of the hill? I am doing a project for my science fair and I sent 5 wheels down a hill. I thought the biggest wheel would go fastest but it didn't. I don't know why. The middle wheel wheel went the fastest most often. It was right in the middle of the weight and diameter. The smallest and lightest wheel went the same speed as the heaviest and biggest wheel.

I know the diameter and masses of the wheels. The length of the hill and the degrees of the slope. Is there a formula that can tell me how fast it should go? I did not push it, I let all the wheels roll just by letting go of them so there wasn't any force. The largest wheel is 63mm diameter and weighs 4 ounces. The smallest is 48mm and weighs 2 ounces. Going down a 10 foot ramp with no wind and no pushing, a 90 degree angle. the small one finishes at 7.8 seconds and the large one at 8.7'

No matter how many times I roll the wheels down the hill, I get different results each time. It's an 8ft slide and they are skateboard wheels with a hole in the middle. they are the same material. I thought the bigger wheel would win more often but it doesn't.


I'm really confused because I thought the results would be the same each time.

I did a slow motion video and showed them all rolling at the same time. Once they left the slide and got into the air, the bigger wheels went in front of the small wheels. I think this is because they have great mass and were propelled further. But why do they all reach the bottom at the same time? Is it because the slide was too short? I did 4 ft, 8ft and 10ft.

Hello and welcome to the forums.

You are investigating the fact that all items (if there is not air resistance) fall at the same speed. This was first discovered by Galileo http://en.wikipedia.org/wiki/Galileo_Ga ... ing_bodies. The speed, distance traveled and acceleration are all calculated using the kinematic equations: http://www.physicsclassroom.com/class/1 ... em-Solving.

In your particular case, there are several factors influencing the speed of your wheels rolling down the hill. Besides the air resistance, there is the rolling resistance and the wobble of the wheels. In other words, you have introduced a lot of uncontrolled variables, making it very difficult to get accurate readings. You could try making a track the fit the wheels in such a way as to reduce wobble. You could use wheels all of the same size, but different weights (which should all end up with the same speed.) This experiment could go many directions, it's up to you. Please let us know what you decide to do.

Best, Keith

In addition to kgudger's points (which are all very valid considerations), you need to understand the concept of "Moment of Inertia" (http://en.wikipedia.org/wiki/Moment_of_inertia, and for an easier to understand explanation: http://www.batesville.k12.in.us/physics ... e_roll.htm). This is the major determinant of the different accelerations you'll see from round objects rolling down inclined planes.

Basically, the size doesn't matter by itself, and the weight doesn't matter by itself, but the distribution of the mass around the object makes a big difference.

(I've provided a wikipedia link as a useful starting point, but please remember that it's not considered good form to use encyclopedias as sources in research papers... follow the links to the primary sources and cite those if you're writing about this).