Understanding Forces and Motion in a Translating and Rotating Ring

In summary, this is a problem from a FE review manual involving a translating and rotating ring with specific mass, angular and translational speeds, and coefficient of friction. The outside radius is provided as 3 cm. The solution involves summation of forces in the x and y directions and finding the angular acceleration and velocity. However, there is confusion about the sign of angular acceleration and the use of tangential component in the solution.
  • #1
gator286
2
0
1)Problem statement
A translating and rotating ring of mass 1 kg, angular speed of 500 rpm, and translational speed of 1 m/s is placed on a horizontal surface. The coefficient of friction between the ring and the surface is 0.35.

Outside radius is 3 cm.

This is a problem from a FE review manual, thanks guys.

2)Attempt at a solution.
ΣFx=ma
ΣFy=0 therefore N=mg
From summation of forces in the x direction,a=g/m
ΣM=0,(µmgR)= α I
I=3MR^2
α=µg /(3R)
v= v_0-at
ω= ω_0- αt
This is where I get lost.
 
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  • #2
Ok, this is a scanned solution of the problem according to the book. It's problem 13.

http://img218.imageshack.us/f/002kfv.jpg/

What I don't understand is why is angular acceleration negative, and a is positive. Shouldn't they both be negative? Also, how did they get v = romega, isn't romega the tangential component?
 

FAQ: Understanding Forces and Motion in a Translating and Rotating Ring

What is a translating and rotating ring?

A translating and rotating ring is a physical object that can move in both a linear (translating) and circular (rotating) motion simultaneously. This type of motion is often seen in mechanical systems or in nature, such as the gears of a clock or the movement of planets around a star.

How does a translating and rotating ring work?

A translating and rotating ring works by having two separate types of motion occurring at the same time. The linear motion involves the ring moving in a straight line, while the circular motion involves the ring rotating around a fixed point. Both of these motions are possible because the ring is able to move freely in multiple directions.

What are the applications of translating and rotating rings?

Translating and rotating rings have many applications in engineering and science. They can be used in machinery to transfer motion in different directions, in robotics for complex movements, and in physics experiments to study circular and linear motion simultaneously.

How are translating and rotating rings different from each other?

Translating and rotating rings are different in terms of the type of motion they exhibit. Translating motion involves movement in a straight line, while rotating motion involves movement around a fixed point. Additionally, translating and rotating rings may have different structures and mechanisms for achieving their respective motions.

Are translating and rotating rings used in real-life applications?

Yes, translating and rotating rings are used in many real-life applications. They are commonly found in mechanical systems, such as engines, where they help transfer motion in multiple directions. They are also used in robotics, astronomy, and other fields where complex motion is required.

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