How Does Friction Torque Affect Angular Speed in a Spinning Spherical System?

In summary, a uniform spherical shell with four small masses attached to its outer surface is spinning about an axis. The question is asking for the friction torque needed to reduce its angular speed from 80.0 to 55.0 in a time interval of 35.0. The solution involves using the circular version of Newton's second law and calculating the rate of change of angular momentum.
  • #1
thecombover
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A uniform spherical shell of mass 9.00 with diameter 54.0 has four small masses of mass 2.00 attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses
yf_Figure_10_43.jpg


What friction torque is needed to reduce its angular speed from 80.0 to 55.0 in a time interval of 35.0 ?
 
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  • #2
Welcome to PF!

thecombover said:
… What friction torque is needed to reduce its angular speed from 80.0 to 55.0 in a time interval of 35.0 ?

Hi thecombover! Welcome to PF! :smile:

Circular version of good ol' Newton's second law …

net torque = rate of change of angular momentum …

so how much angular momentum do you need to change? :wink:
 

1) What is the center of mass?

The center of mass is the point at which the entire mass of an object can be considered to be concentrated, and the object will balance perfectly. It is often referred to as the "center of gravity".

2) How is the center of mass calculated?

The center of mass is calculated by finding the weighted average of the positions of all the particles that make up an object. This can be done using the formula:
xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
where xcm is the center of mass, m is the mass of each particle, and x is the position of each particle along a particular axis.

3) Why is the center of mass important?

The center of mass is important because it helps us understand the stability and motion of an object. The location of the center of mass affects how an object will behave when subjected to external forces, such as gravity or collisions. It is also useful in engineering and design, as it can help determine the balance and stability of structures.

4) Can the center of mass be outside of an object?

Yes, the center of mass can be located outside of an object. This typically occurs when the object has an irregular shape or an uneven distribution of mass. For example, a crescent moon has its center of mass located outside of its physical shape.

5) How does the center of mass change when an object moves?

The center of mass will only change if the mass distribution within the object changes. If the object moves without changing its shape or distribution of mass, the center of mass will remain in the same location. However, when an object is in motion, the position of its center of mass can affect its rotational and translational motion.

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