Resultant acceleration Question

[Steelers72]

Homework Statement

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.270rev/s . The magnitude of the angular acceleration is 0.902rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.800m .

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.191s ?

Homework Equations

[/B]
(v*v)/r

Pythagorean theorem

The Attempt at a Solution

Tangential acceleration= angular acceleration*radius
=.902*.400
=.361

centripetal acceleration = (v*v)/r
I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
= (1.11^2)/.400
=3.08

sqrt( (3.08^2)+(.361^2) )
=3.10

However, this apparently is incorrect. What am I doing wrong?

 

[rude man]

Homework Statement

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.270rev/s . The magnitude of the angular acceleration is 0.902rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.800m .

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.191s ?

Homework Equations

[/B]
(v*v)/r

Pythagorean theorem

The Attempt at a Solution

Tangential acceleration= angular acceleration*radius
=.902*.400
=.361

centripetal acceleration = (v*v)/r
I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
= (1.11^2)/.400
=3.08

sqrt( (3.08^2)+(.361^2) )
=3.10

However, this apparently is incorrect. What am I doing wrong?

In calculating tangential velocity and acceleration, are you using correct units for the angular initial speed and acceleration ?

 

[Pierce610]

The method you are followed is correct but not in one point; the question should help:

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.191s ?.

In an accelerate motion of a point upon a circle its tangential velocity changes continuosly; it is no more the value of the initial istant. So the correct formula to use is (v, v0 and a are tangential):

v-v0 = at

t=0.191 s
a = 0.361 m/s^2
v0=0.270 x 0.400 = 0.108 m/s

 

[collinsmark]

Also, (contrary to the numerical work in Pierce610's post), don't forget to convert revolutions to radians.

 

[Steelers72]

sqrt( (.108^2)+(.361^2) )
=.38

Is this the correct set up for the final answer now?

 

[collinsmark]

sqrt( (.108^2)+(.361^2) )
=.38

Is this the correct set up for the final answer now?

That's not the number I got. Please show your steps, including your units.

And again, don't forget to convert the revolutions to radians as an early step.

 

[Pierce610]

thanks sincerely to have correct me; I've forgotten to convert them.

 

[Steelers72]

Also, (contrary to the numerical work in Pierce610's post), don't forget to convert revolutions to radians.

Based on my original post, which step did I mess up

centripetal acceleration = (v*v)/r
I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
= (1.11^2)/.400
=3.08

 

[ehild]

Based on my original post, which step did I mess up

centripetal acceleration = (v*v)/r
I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
= (1.11^2)/.400
=3.08

Your tangential acceleration is wrong: revolutions have to be converted to radians.

 

[rude man]

Based on my original post, which step did I mess up

centripetal acceleration = (v*v)/r
I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
= (1.11^2)/.400
=3.08

You had better listen to posts 2, 4 and 9 unless you meant radians instead of revolutions in your original post.

 

[Steelers72]

Your tangential acceleration is wrong: revolutions have to be converted to radians.

So I have to convert 1.11 revolutions to radians?
so would it be 1.11 rev*2piradians/rev ?

 

[rude man]

So I have to convert 1.11 revolutions to radians?
so would it be 1.11 rev*2piradians/rev ?

Yes, assuming the 1.11 number was derived correctly (I'm not looking at the problem now).
In general, take a leaf from this book: all units must be compatible. In most cases for you this means the units of the rationalized mks system, aka SI (Sysème Internationale).

 

[ehild]

So I have to convert 1.11 revolutions to radians?
so would it be 1.11 rev*2piradians/rev ?

No.
The tangential acceleration was wrong. The angular acceleration was given as 0.902 rev/s². Convert it to radians/s².

 

[Steelers72]

No.
The tangential acceleration was wrong. The angular acceleration was given as 0.902 rev/s². Convert it to radians/s².

so .902revs/s^2 *2piradians/rev=1.80pi radians/s^2

(1.80^2)/.400
=8.1

sqrt( (8.1^2)+(.361^2) )
=8.11

Is this correct?

 

[ehild]

so .902revs/s^2 *2piradians/rev=1.80pi radians/s^2

(1.80^2)/.400
=8.1

sqrt( (8.1^2)+(.361^2) )
=8.11

Is this correct?

It is wrong. How much is 0.902*2pi?
How do you get the linear acceleration from the angular acceleration?

 

[Steelers72]

It is wrong. How much is 0.902*2pi?
How do you get the linear acceleration from the angular acceleration?

5.67pi ...i don't understand why I keep getting a wrong answer from my calculator. Thanks. So 5.67

(5.67^2)/.400
=80.37

sqrt( (80.37^2)+(.361^2) )
=80.37

? this ok now?

 

[ehild]

5.67pi ...i don't understand why I keep getting a wrong answer from my calculator. Thanks. So 5.67

(5.67^2)/.400
=80.37

sqrt( (80.37^2)+(.361^2) )
=80.37

? this ok now?

No. Use the units, you will see that it is wrong. What is the unit of the angular acceleration? What is the unit of the linear acceleration?
What are all those numbers you wrote?
What do you mean with (5.67^2)/.400? What do you think it is?