1. compare these objects:
object alpha is a hoop of mass 55kg and radius .24m;
object bravo is a disk of mass 86kg and radius .24m;
object charlie is a sphere of mass 112kg and radius .24m.
a) calculate the rotational inertias of each object?

|hoop |disk |sphere
| | |
| | |
| | |
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b) which object would win a race down an inclined plane?

I = 3.168

I = 2.48

I = 2.58

Charlie

Object Alpha is a hoop of mass 55kg and radius 0.24m

Formula to use

I = (m)(r)(r)

I = 55(0.24)²

I = 3.168

Object Bravo is a disk of mass 86kg and radius .24m

Formula to use

I = 1/2(m)(r)(r)

I = 1/2(86)(0.24)²

I = 2.48

Object Charlie is a sphere of mass 112kg and radius .24m

Formula to use

I = 2/5(m)(r)(r)

I = 2/5(112)(0.24)²

I = 2.58

As solid(sphere) object will always roll down the ramp faster than a hollow(disk, hoop) object of the same shape so Charlie will win the race down the incline plane

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