Calculating Angular Momentum: Mass, Radius, and Frequency Considerations

In summary, to find the angular momentum of a turntable with a mass of 4.96 kg and a radius of 0.092 m spinning at a frequency of 0.53 rev/s, we use the formula L = Iω, where I is the moment of inertia and ω is the angular velocity in radians per second. After converting the frequency to radians per second, the correct answer is 0.0699 (kgm^2)/s.
  • #1
jmb07
27
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A turntable has mass 4.96 kg and a radius of 0.092 m and is spinning with a frequency of 0.53 rev/s. What is the angular momentum??

As simple as this problem seems, I just cannot seem to get the correct answer...here is what i have so far:

I (for a disc) = (1/2)(mr^2)
L = I(omega)
I also know that angular momentum = frequency x I

So,
0.53rev/s(.5 x 4.96kg x 0.092^2) = 0.011 (kgm^2)/s
However the correct answer is 0.0699...what am i doing wrong?
 
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  • #2
jmb07 said:
L = I(omega)
I also know that angular momentum = frequency x I
L = Iω, where ω is in radians/sec.

So,
0.53rev/s(.5 x 4.96kg x 0.092^2) = 0.011 (kgm^2)/s
However the correct answer is 0.0699...what am i doing wrong?
Convert to proper units.
 
  • #3
The frequency is in revolutions per second; you need to convert it into radians per second. The conversion factor is [itex]2\pi\ \text{radians} = 1\ \text{revolution}[/itex].
 
  • #4
thanks!
 

FAQ: Calculating Angular Momentum: Mass, Radius, and Frequency Considerations

What is angular momentum and how is it defined?

Angular momentum is a physical quantity that reflects the amount of rotational motion of an object. It is defined as the product of an object's moment of inertia and its angular velocity.

How is angular momentum conserved in a closed system?

In a closed system, the total angular momentum remains constant, meaning it is conserved. This is due to the law of conservation of angular momentum, which states that the total angular momentum of a system cannot change unless an external torque is applied.

What is the difference between angular momentum and linear momentum?

Angular momentum and linear momentum are both measures of an object's motion, but they differ in direction. Linear momentum is a measure of an object's motion in a straight line, while angular momentum is a measure of an object's rotational motion.

How does angular momentum impact the rotation of a spinning object?

The greater the angular momentum of a spinning object, the harder it is to change its rotation. This is due to the principle of conservation of angular momentum, which states that an object will maintain its angular momentum unless acted upon by an external force.

What are some real-world examples of angular momentum?

There are many examples of angular momentum in our daily lives, such as the rotation of a spinning top, the motion of a spinning bicycle wheel, or the rotation of the Earth around its own axis. Additionally, the orbits of planets and satellites also involve angular momentum.

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