Average Acceleration of a Fly on a Rotating Hand

[TheronSimon]

Homework Statement

A fly sitting on the end of the second hand of a clock is traveling in a circle. The second hand has a length of 25 cm. Calculate the average acceleration of the fly.

Homework Equations

The Attempt at a Solution

\
since only one measurment is given who would i calculate for acceleration?

 

[DeIdeal]

Do you know the equation for centripetal acceleration? It could be useful here, seeing as the fly is traveling in a circle ... ; )

After that you should consider the velocity: It's a clock, you should be able to figure out how fast the hands are moving. And whether they are accelerating or not.

Spoiler

Sorry if I gave out too much or not enough information, I'm not sure what's usually considered an appropriate amount.

 

[TheronSimon]

lol i didnt even think of the fact that its a clock :P
so

a= 4$\pi$² R / T²

a = 4$\pi$² * 0.24 / 60²

a= 0.0027

 

[gneill]

Remember also that acceleration is a vector quantity; it has both magnitude and direction. You're being asked to find the average acceleration...

 

[TheronSimon]

0.0027 m/s^2? lol I am sorry i don't know what else you would mean

 

[DeIdeal]

0.0027 m/s^2? lol I am sorry i don't know what else you would mean

Yeah, if the question actually asks for average acceleration (didn't even notice that earlier, sorry), you should definitely consider the direction of the acceleration as well.

 

[TheronSimon]

but what do you mean by that its going in a circle what direction could it have?

 

[TheronSimon]

directed towards the centre?

 

[TheronSimon]

hello? any help?

 

[emailanmol]

Think of the clock being at 3 o clock.Acceleration is towards the centre i.e towards negative x axis.

At 6 o clock acceleration is towards centre again but along positive y axis.

So although the magnitude is constant , the direction isn't which has to be taken into consideration else you will get the wrong answer.( For eg when the particle has covered an entire circle avg acceleration is 0 and not the value you got.
This is because accelerations at exactly opposite diametrical ends cancel out.
Like acceleration at 6 o clock is upwards and is canceled by the acceleration at 12 o clock which is downwards.
All such pairs like 12:05 amd 6:35 cancel out to yield 0 as average acceleration

You have found the avg magnitude of acceleration.Not avg acceleration)

to find avg acceleration

Write the value of position vector at any point in terms of sin(m) and cos (m).(here m is angle of rotation.I am via cell so can't type theta).

Differentiate it twice wrt time to obtain the acceleration vector at any m.

Then we will guide you further on how to obtain avg. acceleration from the equation you just obtained

 

[shyguy79]

Think of the right hand rule for centripetal acceleration... what direction does the hands on a clock go and what is the resultant direction?

 

[gneill]

Suppose the acceleration of the fly is always directed towards the center of the clock face. How would you determine an average for the acceleration? What does "average" mean?

 

[TheronSimon]

so i asked my teacher about it and it wants centripetal acceleration not average

 

[emailanmol]

Even if it asks just the acceleration,

Your answer states just the magnitude.
You will need to write it in terms of vectors to get the right answer :-)

(p.s towards the centre is correct but what is it in terns of vector like i and j)