Finding Rotational Kinetic Energy of Sphere on Ramp

In summary, the total kinetic energy of Inga's spherical and solid spare head that was rolled down a 4 m ramp at a speed of 4.5 m/s, with a mass of 4.5 kg, is approximately 63.79 J. There may be some slight variations in the calculation based on the radius of the sphere, but the ratio of rotational and linear kinetic energy remains constant.
  • #1
joel amos
104
0

Homework Statement


If Inga, the Laboratory Assistant, rolls a spare head down a 4 m ramp because it was spherical and solid and too heavy at 4.5 kg at a speed of 4.5 m/s, what was its total kinetic energy?


Homework Equations


KE = (1/2) I ω^2
I = (2/5) MR^2

The Attempt at a Solution


Basically, I'm not sure how to solve this without the sphere's radius. Any help, solutions, or hints would be highly appreciated.
 
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  • #2
Just go ahead with the algebra and you should find the radius cancels out. The rotational KE of a sphere is in fixed ratio to its linear KE, regardless of radius.
 
  • #3
So does this look correct:

KE = (1/2)(4.5 kg)(4.5m/s)^2 + (1/2)(2/5)(4.5)r^2[(4.5m/s)/r]^2
KE = 6.75 J + 18.225 J
KE = 24.98 J
 
  • #4
Where'd that 6.75 J come from?
 
  • #5
izelkay said:
Where'd that 6.75 J come from?
Hmm..I too am now wondering the same.

Is this better:

KE = 45.453 J + 18.225 J
KE = 63.69 J
 
  • #6
joel amos said:
Hmm..I too am now wondering the same.

Is this better:

KE = 45.453 J + 18.225 J
KE = 63.69 J
Still a bit low. I get 45.56+18.23=63.79
 
  • #7
haruspex said:
Still a bit low. I get 45.56+18.23=63.79

That's also what I'm getting. Joel, I think you're not plugging into your calculator correctly.
 

What is rotational kinetic energy?

Rotational kinetic energy is the energy possessed by an object due to its rotation around an axis.

How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is KE = (1/2)Iω^2, where KE is kinetic energy, I is the moment of inertia, and ω is the angular velocity.

What factors affect the rotational kinetic energy of a sphere on a ramp?

The rotational kinetic energy of a sphere on a ramp is affected by the mass of the sphere, its radius, the angle of the ramp, and the speed at which it is rolling.

What is the relationship between rotational kinetic energy and translational kinetic energy?

Rotational kinetic energy and translational kinetic energy are both forms of kinetic energy and are interrelated. As the rotational kinetic energy of a sphere increases, so does its translational kinetic energy, and vice versa.

Can rotational kinetic energy be converted into other forms of energy?

Yes, rotational kinetic energy can be converted into other forms of energy such as heat or potential energy. This is known as the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

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