Is this tangential velocity or angular velocity?

In summary, the conversation revolves around a homework question that involves finding the centripetal acceleration of a rotating rod with a speed of 2010m/s and a length of 15cm. There is a discussion about whether the speed given is angular or tangential velocity, and how to differentiate between the two. The group also debates whether the radius or diameter of the rod is 15cm. Eventually, they determine that the radius is 15cm and the problem can be solved. One member also mentions a similar problem with a length of 15.3cm.
  • #1
donjt81
71
0
Here is the homework question...

According to the Guinness Book of World Records, the highest rotary speed ever attained was 2010m/s(4500mph). The rotating rod was 15cm(6in.) long. Assume the speed quoted is that of the end of the rod. What is the centripetal acceleration of the end of the rod?

So I think since they say rotary speed they are talking about angular velocity here. so i would say angular velocity (w) = 2010m/s. Is this correct? or is it tangential velocity (v) = 2010m/s?

is there a certain way to tell the difference between tangential velocity and angular velocity in a question.

Thanks in advance
 
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  • #2
donjt81 said:
is there a certain way to tell the difference between tangential velocity and angular velocity in a question.
Thanks in advance
Yes, look at the unit. Here it is 2010 m/s. This is a linear velocity unit. angular velocity is in angular units per unit of time, such as "rotations per second", "revolutions per minute", "degrees per second." The SI unit for [tex]\omega[/tex] is radians per second.
 
  • #3
Thank you that makes it easier to tell.

Also I was looking at it again and another question popped in my head.

When i first looked at the problem I was assuming that radius=15cm but then after looking at it some more i was thinking is it diameter = 15cm or is it radius = 15cm

does anyone know?
 
  • #4
There is no way that the diameter is 15 cm. Either the rod is rotating about its end and the radius is 15 cm, or the rod is roatating about its middle, and the radius will be 7.5 cm.
 
  • #5
There is no way that the diameter is 15 cm
and the radius will be 7.5 cm.


umm... that's the same thing. diameter is 15 means that radius is 15/2=7.5

soooo... is'nt that contradicting statements.
 
  • #6
donjt81 said:
umm... that's the same thing. diameter is 15 means that radius is 15/2=7.5
soooo... is'nt that contradicting statements.
Um, yes I was, um,... seing if...

I was checking to see if... you were...paying attention.

Very good.

[I have no idea what I was thinking last night! ..it happens]
 
  • #7
no worries
thanks for your help.
i was able to solve the problem
 
  • #8
Did you figure it out or no? I'm doing that exact problem now, except it's 15.3 not 15. is it rotating around the middle or about the end?

ahhh. lame physics lol.
 

1. What is tangential velocity and angular velocity?

Tangential velocity is the measure of the speed at which an object is moving in a circular path. It is always tangent to the circle at any given point. Angular velocity, on the other hand, is the measure of how fast an object is rotating around a fixed point. It is measured in radians per unit time.

2. How do tangential velocity and angular velocity relate to each other?

Tangential velocity and angular velocity are related by the radius of the circular path. The tangential velocity is equal to the product of the angular velocity and the radius of the circle. This means that the closer an object is to the center of the circle, the slower its tangential velocity will be compared to an object on the outer edge with the same angular velocity.

3. Can an object have both tangential velocity and angular velocity?

Yes, an object can have both tangential velocity and angular velocity at the same time. This is often the case for objects moving in circular motion, such as a Ferris wheel or a spinning top. The tangential velocity determines the speed at which the object is moving around the circle, while the angular velocity determines how quickly the object is rotating.

4. How are tangential velocity and angular velocity measured?

Tangential velocity is measured in units of distance per unit time, such as meters per second. Angular velocity is measured in units of radians per unit time, such as radians per second. Both of these velocities can be calculated using equations that take into account the object's speed and the radius of the circular path it is moving along.

5. Why is it important to understand the difference between tangential velocity and angular velocity?

Understanding the difference between tangential velocity and angular velocity is important in many areas of science and engineering. For example, in mechanics, these velocities are used to calculate the forces acting on an object in circular motion. In astronomy, they are used to study the motion of planets and other celestial bodies. In robotics, they are used to program movements of robotic arms and other machinery. Overall, understanding these concepts can help us better understand the world around us and make accurate calculations and predictions.

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