Question involving clockwise angular movement

In summary, the wheel in this problem has a diameter of 2.00 m and is rotating with a constant angular acceleration of 4.00 rad/s^2 in a vertical plane. Point P on the rim starts at rest at t=0 with its radius vector making an angle of 57.3° with the horizontal. At t=2.00 s, we are asked to find the linear speed and acceleration of point P. The linear speed is found to be 8 m/s and the acceleration is 64 m/s^2. However, the textbook states that the acceleration should be negative, indicating a clockwise direction. This is because the unit vector for radial acceleration points outwards, while centripetal acceleration points inwards
  • #1
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Homework Statement
A wheel 2.00 m in diameter lies in a vertical plane and rotates with a constant angular acceleration of 4.00 rad/s^2. The wheel starts at rest at t= 0, and the radius vector of point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find
(b) the linear speedand acceleration of the point P
Relevant Equations
v=r##w##
ar=r##w##^2
at=r*alpha
v=1.00*8=>v=8 rad/s

ar=>100*8^2=>ar=64 rad/s^2
at=1.00*4=>at=4 rad/s^2

The only question I have is ar=-64 rad/s^2, not 64 rad/s^2 as I calculated. I believe this is because the wheel is accelerating in a clockwise direction. However this is not indicated by the mathematical equation. How do I detect that the acceleration is clockwise?
 
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  • #2
The radial acceleration ##a_r## is positive when it points away from the center and negative when it points towards the center. Which of the two is the case here?
 
  • #3
as2528 said:
Homework Statement:: A wheel 2.00 m in diameter lies in a vertical plane and rotates with a constant angular acceleration of 4.00 rad/s^2. The wheel starts at rest at t= 0, and the radius vector of point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find
(b) the linear speedand acceleration of the point P
Relevant Equations:: v=r##w##
ar=r##w##^2
at=r*alpha

v=1.00*8=>v=8

ar=>100*8^2=>ar=64
at=1.00*4=>at=4

The only question I have is ar=-64, not 64 as I calculated. I believe this is because the wheel is accelerating in a clockwise direction. However this is not indicated by the mathematical equation. How do I detect that the acceleration is clockwise?
You really should quote units everywhere as appropriate.

The question as posted does not say whether the acceleration is clockwise or anticlockwise, nor which of four possible positions P might start at.

Are you asking whether ar should be + or -, or are you saying the given answer is minus, and you want to know why?
For the purpose of finding the magnitude of the total acceleration it isn't going to matter. Are you supposed to specify the direction as well?
 
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  • #4
haruspex said:
You really should quote units everywhere as appropriate.

The question as posted does not say whether the acceleration is clockwise or anticlockwise, nor which of four possible positions P might start at.

Are you asking whether ar should be + or -, or are you saying the given answer is minus, and you want to know why?
For the purpose of finding the magnitude of the total acceleration it isn't going to matter. Are you supposed to specify the direction as well?
ar is supposed to be minus and I want to know why. I am supposed to specify the direction as part of the question although it is not explicitly said. I have put in the units now.
 
  • #5
I thought it must always point towards the center though? I thought that otherwise the object should fly off in a tangent line. The textbook said that if the wheel is accelerating in a clockwise direction acceleration is negative, and if it is accelerating in a counterclockwise direction it is positive.
 
  • #6
as2528 said:
ar is supposed to be minus and I want to know why
In vector form, radial acceleration is often written as a multiple of the radius vector, ##\vec a_r=a_r\hat r##. Since that unit vector points outwards and centripetal acceleration points inwards the coefficient will be negative.
However, I see no specification that it should be expressed in that form.
as2528 said:
I am supposed to specify the direction as part of the question
Again, it is unclear how the direction is to be expressed.
In Cartesian coordinates, it will depend where P is at the time, which will in turn depend on which of the four possible starting positions you choose.

Have you quoted the whole question, word for word?
 
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  • #7
haruspex said:
In vector form, radial acceleration is often written as a multiple of the radius vector, ##\vec a_r=a_r\hat r##. Since that unit vector points outwards and centripetal acceleration points inwards the coefficient will be negative.
However, I see no specification that it should be expressed in that form.

Again, it is unclear how the direction is to be expressed.
In Cartesian coordinates, it will depend where P is at the time, which will in turn depend on which of the four possible starting positions you choose.

Have you quoted the whole question, word for word?
Yes this is the complete question. In part a I was just meant to find the number of revs the tire makes during the motion. I don't think that had bearing on this part of the question though.

I didn't understand why it was meant to be negative since it didn't explicitly ask for it ever, and I thought that there might be some physics that I was missing. In the answers to the question though it does provide a negative sign on the acceleration which is when I discovered that it was meant to be negative.
 
  • #8
haruspex said:
In vector form, radial acceleration is often written as a multiple of the radius vector, ##\vec a_r=a_r\hat r##. Since that unit vector points outwards and centripetal acceleration points inwards the coefficient will be negative.
However, I see no specification that it should be expressed in that form.

Again, it is unclear how the direction is to be expressed.
In Cartesian coordinates, it will depend where P is at the time, which will in turn depend on which of the four possible starting positions you choose.

Have you quoted the whole question, word for word?
Also it does appear that every answer given online other than the one from the textbook has a positive value just like I calculated. I guess it must be a mistype.
 
  • #9
as2528 said:
Also it does appear that every answer given online other than the one from the textbook has a positive value just like I calculated. I guess it must be a mistype.
Maybe, but as I explained, minus does make sense if you assume a fairly standard convention regarding the representation of radial acceleration.
 
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  • #10
haruspex said:
Maybe, but as I explained, minus does make sense if you assume a fairly standard convention regarding the representation of radial acceleration.
I'll take the textbook and the minus sign as right then. Thanks!
 

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