Help with, I am sure, a really simple circular motion problem

In summary, the conversation discusses a physics question about angular velocity and radians. The answer involves using the formula ω = θ/T and simplifying it to ω = v(tangential)/l. The individual asking the question is struggling to understand the concept and appreciates any help. The expert provides additional resources for clarification and explains that one full turn per second equals 6.28... radians/second.
  • #1
Nathi ORea
82
22
Misplaced Homework Thread
Summary: I am just trying to go through a Brilliant physics unit. I came across this axe throwing question which I don't get at all how they get the answer.

Screen Shot 2022-09-15 at 3.41.38 pm.png

You can see the answer there.

So their explanation is;

'In going around the circle, the red point moves through an angle of
θ = 360° or θ = 2π, and its angular velocity is simply ω = θ/T
'

Now I actually thought that would be the answer.. Just 2πl/T, but they continue

'ω = θ/T
= 2π X v(tangential)/l
= v(tangential/
l'

I guess I am stuck on how they got from ω = θ/T to ω = 2π X v(tangential)/l

I can see how they simplified ω = 2π X v(tangential)/l to ω = v(tangential/l'

I am just doing this Brilliant course because I find it interesting and want to learn more about how our world works. I am certainly no maths wiz.. lol. but I appreciate any help.
 
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  • #2
[tex]\omega=\frac{\theta}{T}[/tex]
[tex]=\frac{\theta l}{T l}=\frac{\frac{\theta l}{T}}{l}=\frac{v}{l}[/tex]
 
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  • #3
anuttarasammyak said:
[tex]\omega=\frac{\theta}{T}[/tex]
[tex]=\frac{\theta l}{T l}=\frac{\frac{\theta l}{T}}{l}=\frac{v}{l}[/tex]
Thanks for replying.
I think I know why you put an ‘l’ next to theta (because that gives you the actual distance around the circle) but why does T have an ‘l’.

I feel so dumb…lol
 
  • #4
As a math rule
[tex]\frac{a}{b}=\frac{al}{bl}[/tex]
Multiplying a same number to numerator and denominator does not alter the number.
 
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  • #5
##2\pi l=v_{tangential}T=circumference\ of\ circle##, where T is the period of rotation. So, $$T=\frac{2\pi l}{v_{tangential}}$$
 
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  • #8
Nathi ORea said:
Thanks for that. I misunderstood what 'angular velocity' actually meant.

I have been trying to work it out, but the whole angular velocity and radians thing is not coming very intuitively to me at all... lol
You are welcome.
One full turn per second equals 6.28... radians/second.

Circle_radians.gif
 
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Related to Help with, I am sure, a really simple circular motion problem

1. What is circular motion?

Circular motion is the movement of an object along a circular path. This can be seen in objects such as planets orbiting around a star or a car going around a roundabout.

2. How is circular motion different from linear motion?

Circular motion involves an object moving along a curved path, while linear motion involves an object moving in a straight line. In circular motion, the direction of the object is constantly changing, whereas in linear motion, the direction remains constant.

3. What is the difference between tangential and radial acceleration in circular motion?

Tangential acceleration is the change in speed of an object moving along a circular path, while radial acceleration is the change in direction of the object. Tangential acceleration is always perpendicular to the radial acceleration.

4. How do you calculate the centripetal force in circular motion?

The centripetal force is the force that keeps an object moving in a circular path. It is calculated using the formula F = mv^2/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

5. What are some real-life examples of circular motion?

Some examples of circular motion in everyday life include the rotation of a ceiling fan, the motion of a spinning top, and the movement of a Ferris wheel. In nature, circular motion can be seen in the orbit of planets around the sun and the rotation of the Earth on its axis.

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