How Do You Calculate Angular Speed and Velocity of Clock Hands?

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Homework Help Overview

The discussion revolves around calculating the angular speed and angular velocity of the second and hour hands of a clock, specifically in radians per second. Participants explore the definitions and relationships between angular speed and angular velocity, as well as the implications of time intervals in these calculations.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the difference between angular speed and angular velocity, questioning whether they are the same and how to approach the calculations for each hand separately. There are attempts to clarify the relevance of circumference and time in determining angular speed.

Discussion Status

Some participants have provided guidance on the formulas to use for calculating angular speed for each hand, while others are still exploring the implications of time and the relationship between angular speed and angular velocity. Multiple interpretations of the problem are being discussed, particularly regarding the time taken for each hand to complete a revolution.

Contextual Notes

There are ongoing questions about the units involved in the calculations and the assumptions regarding the time intervals for the second and hour hands. Participants are also addressing potential confusion about the relationship between radians and the radius of the circle.

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Homework Statement


For the second handand the hour hand of a running clock, find the angular speed and the angular velocity. (in rad/sec)


Homework Equations



Circumference = 2 x pix radius

360 degrees = 1 revolution.

The Attempt at a Solution



I know that the circumference can be altered to make radians like this C = 2 x pi / rad .

But is the angular speed the same as the angular velcority? Or is it asking for me to find the ang speed and velocity for the second hand anhour hand seperate?

I know that the circumference is 3,600s. So would you end up for the angular speed taking the 3,600s x 2 x pi / rad ? Or would the angular speed and velocity be the exact same for both the second and hour hand?

I'm mainly wanting to learn how to do the problems. :]
 
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The angular speed is the magnitude of the angular velocity. The angular velocity is a vector quantity (well, technically a pseudo-vector quantity, but that's probably a nit-pick at this juncture).

Both angular speed and angular velocity have units of radians per second (rad/sec). How many radians in a full circle (say as a radius vector sweeps around it)? Do the number of radians depend upon the radius or diameter of the circle?
 
Circumference = 2 x pix radius

The circumference isn't relevant here. You're trying to find angular speed. That's how fast the hand rotates, in radians per second; it's not how fast the hand is moving in m/s.

But is the angular speed the same as the angular velcority? Or is it asking for me to find the ang speed and velocity for the second hand anhour hand seperate?

Yes, angular speed is just another name for angular velocity.

I know that the circumference is 3,600s. So would you end up for the angular speed taking the 3,600s x 2 x pi / rad ? Or would the angular speed and velocity be the exact same for both the second and hour hand?

How can the circumference be 3600s, which has units of time?

Angular speed is the angle spanned by one revolution--which is 2*pi--divided by the time it takes to complete that revolution. How long does the second hand take to complete one revolution? The hour hand?
 
ideasrule said:
The circumference isn't relevant here. You're trying to find angular speed. That's how fast the hand rotates, in radians per second; it's not how fast the hand is moving in m/s.



Yes, angular speed is just another name for angular velocity.



How can the circumference be 3600s, which has units of time?

Angular speed is the angle spanned by one revolution--which is 2*pi--divided by the time it takes to complete that revolution. How long does the second hand take to complete one revolution? The hour hand?

Oh so it is asking for them to be seperate. Isn't it that because in 1hr it is 3600s. Or is that using it to convert it to seconds for part of the rad?
 
gneill said:
The angular speed is the magnitude of the angular velocity. The angular velocity is a vector quantity (well, technically a pseudo-vector quantity, but that's probably a nit-pick at this juncture).

Both angular speed and angular velocity have units of radians per second (rad/sec). How many radians in a full circle (say as a radius vector sweeps around it)? Do the number of radians depend upon the radius or diameter of the circle?

So basically a radian is the same as a radius but that the radius halfway and the length of that usually is used to make up ever how many wil go around the circle just like 2 pi r which would be 6.28 radians in a circle with involving the circumference? In a full circle without any numbers but the equation for circumference it would be 6.28 rad.

The number of radians depenmds upon the radius of the circle.
 
ideasrule said:
The circumference isn't relevant here. You're trying to find angular speed. That's how fast the hand rotates, in radians per second; it's not how fast the hand is moving in m/s.



Yes, angular speed is just another name for angular velocity.



How can the circumference be 3600s, which has units of time?

Angular speed is the angle spanned by one revolution--which is 2*pi--divided by the time it takes to complete that revolution. How long does the second hand take to complete one revolution? The hour hand?

Oh! So what your saying is to take 2 x pi divide by 3600 sec which is 22,608 sec. But the problem is asking to put the asnwer into rad/sec. So your saying to find it in revolutions/sec first and then convert it to rads/sec?
 
You've got multiplication and division mixed up. 2*pi / 3600 = 0.0017 rad / s [Notice the units]
 
But so then wouldn't the second hand and the hour hand both be the same since they have to go by 12 intervals? Oh my bad, because its rads over seconds. Much Thanks! :]
 
They are asking you for to find the angular velocity.

The formula you will be using is 2*pi/seconds

a.) the second hand
2*pi/60 seconds
(becaus there are 60 seconds in a minute)
= .1047197551 rad/s

b.) the minute hand
2*pi/3600 seconds
(because i had to multiply 60*60 to see how many seconds were in 60 minutes)
=0.0017453293 rad/s

c.) the hour hand
2*pi/43200
(becaue there are 12 hours and there are 60 minutes in an hour so i converted to minutes which was 60*60=720; and then i had to multiply 720*60=43200 to give the seconds in 12 hours)
=1.45*10^ -4=0.000145

to find the angular acceleration

d.) the acceleration is constant on a clock that is working properly so the acceleration will be 0 because its not slowing down or speeding up its the sameI hope this will help you out...
 
  • #10
naimagul said:
They are asking you for to find the angular velocity.

The formula you will be using is 2*pi/seconds

a.) the second hand
2*pi/60 seconds
(becaus there are 60 seconds in a minute)
= .1047197551 rad/s

b.) the minute hand
2*pi/3600 seconds
(because i had to multiply 60*60 to see how many seconds were in 60 minutes)
=0.0017453293 rad/s

c.) the hour hand
2*pi/43200
(becaue there are 12 hours and there are 60 minutes in an hour so i converted to minutes which was 60*60=720; and then i had to multiply 720*60=43200 to give the seconds in 12 hours)
=1.45*10^ -4=0.000145

to find the angular acceleration

d.) the acceleration is constant on a clock that is working properly so the acceleration will be 0 because its not slowing down or speeding up its the same


I hope this will help you out...


Oh so you would convert 12 then, thankyou very much. This helped me immensley!
 
  • #11
Kikki:) said:
Oh so you would convert 12 then, thankyou very much. This helped me immensley!

you are always welcome
 

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