You and some fellow physics students decide to investigate the concept of moment of inertia for yourselves. You set up an experiment in which you race a number of similarly sized objects down a frictionless ramp. The angle of the ramp is theta = 20 degrees and the distance the objects slide or roll down the ramp is s = 1 m. All the objects are made out of the same type of steel and so are of uniform density. The objects you have are: 1) a solid cube measuring 5 cm on a side and having a mass of 0.98 kg; 2) a solid sphere of 2.5 cm radius and having a mass of 0.52 kg; 3) a hollow sphere with an outer radius of 2.5 cm, an inner radius of 1.25 cm, and a mass of 0.45 kg; 4) a spherical shell of 2.5 cm radius and 0.06 kg mass; 5) a solid cylinder having a radius of 2.5 cm, a length of 5 cm, and a mass of 0.77 kg; 6) a hollow cylinder of 2.5 cm outer radius, 1.25 cm inner radius, 5 cm length, and 0.58 kg mass; and 7) and tube (cylindrical shell or ring) having a radius of 2.5 cm, a length of 5 cm, and a mass of 0.06 kg. Determine how long it takes for each object to descend the ramp and rank the objects in order from fastest to slowest. What can you say about the dependence of your results on the mass and physical dimensions (size) of the objects?
You and some fellow physics students decide to investigate the concept of moment of inertia for yourselves. You set up an experiment in which you race a number of similarly sized objects down a frictionless ramp. The angle of the ramp is theta = 20 degrees and the distance the objects slide or roll down the ramp is s = 1 m.
All the objects are made out of the same type of steel and so are of uniform density.
The objects you have are:
1) a solid cube measuring 5 cm on a side and having a mass of 0.98 kg;
2) a solid sphere of 2.5 cm radius and having a mass of 0.52 kg;
3) a hollow sphere with an outer radius of 2.5 cm, an inner radius of 1.25 cm, and a mass of 0.45 kg;
4) a spherical shell of 2.5 cm radius and 0.06 kg mass;
5) a solid cylinder having a radius of 2.5 cm, a length of 5 cm, and a mass of 0.77 kg;
6) a hollow cylinder of 2.5 cm outer radius, 1.25 cm inner radius, 5 cm length, and 0.58 kg mass; and
7) and tube (cylindrical shell or ring) having a radius of 2.5 cm, a length of 5 cm, and a mass of 0.06 kg.
Determine how long it takes for each object to descend the ramp and rank the objects in order from fastest to slowest.
What can you say about the dependence of your results on the mass and physical dimensions (size) of the objects?
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