Calculating angular momentum of a sphere

In summary, the conversation was about a problem involving a solid steel sphere spinning on an axis with a given period and calculating its angular momentum. The solution involved using equations for angular velocity, moment of inertia, and volume, and the result was found to be 0.000140973359 kg/m^2/s. However, there was a mistake in the unit of the moment of inertia, which should be in kgm^2, and the result should be given in normal form with two significant digits.
  • #1
BBC of peace
2
0
I've tried this problem at least 10 times using the equations in my book and I keep getting the same answer. What am I doing wrong?

Homework Statement


A solid steel sphere of density 7.6 g/cm3
and
mass 0.2 kg spin on an axis through its center
with a period of 1.5 s.
Given Vsphere =4/3π^3, what is its angular momentum?
Answer in units of kg m2/s

Homework Equations


Angular momentum=Moment of inertia*angular velocity
Moment of inertia for a solid sphere=2/5MR^2
Volume=Mass/Density
Vsphere=4/3π^3
Angular velocity=2π/period

The Attempt at a Solution


Angular velocity=2π/1.5= 4.18879rad/s
Volume of sphere=.2kg/.0076kg/cm^3=26.3158cm^3
Radius of sphere=[26.3158cm^3/(4π/3)]^(1/3)=1.845197cm =0.01845197meters
I=(2/5)(.2kg)(0.01845197m)^2=.000027238 kg/m^2
Angular momentum=(.000027238kg/m^2)(4.18879rad/s)=0.000140973359kg/m^2/s

I thought my answer was correct but my university's homework page keeps telling me that is it wrong. Anyone know where I am going wrong in this problem?
 
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  • #2
Nevermind, I guess I typed in the answer wrong. My solution was correct.
 
  • #3
The numerical result is correct, but the unit is wrong. The unit of moment of inertia is kgm2. And give the result in normal form (scientific notation) with two significant digits.

ehild
 

1. How do you calculate the angular momentum of a sphere?

To calculate the angular momentum of a sphere, you would use the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

2. What is the moment of inertia?

The moment of inertia, represented by the letter I, is a measure of an object's resistance to rotational motion. It takes into account the distribution of mass around the axis of rotation.

3. How do you find the moment of inertia of a sphere?

The moment of inertia of a sphere can be found using the formula I = (2/5)mr², where m is the mass of the sphere and r is the radius.

4. What is the angular velocity?

Angular velocity, represented by the symbol ω, is a measure of the rate of change of angular displacement over time. It is measured in radians per second.

5. How does angular momentum affect the motion of a sphere?

Angular momentum is a conserved quantity, meaning it remains constant unless acted upon by an external torque. In the case of a sphere, angular momentum affects its rotational motion and can be used to calculate the torque needed to change its rotation.

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