Calculating Angular Acceleration of Wheel of Radius R Given Vector of Tot. Acc.

In summary, the conversation discusses how to calculate the angular acceleration of a wheel of radius R, given that its vector of total acceleration at a point on its perimeter forms an angle of pi/6 with the tangential acceleration at t=1sec after the body has begun its motion. The solution involves using the dot product/product of lengths to yield cosine 30, which then leads to the calculation of dw/dt=sqrt(3)w^2. There is also a suggestion to use the ratio of the radial and tangential components to solve the problem.
  • #1
peripatein
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How may I calculate the angular acceleration of a wheel of radius R given that its vector of total acceleration of a point on its perimeter forms an angle of pi/6 wrt the tangential acceleration at that point at t=1sec after the body has begun its motion?

My attempt at a solution:

a_tot = (-r*w^2,r*dw/dt)
a_tang = (0,r*dw/dt)
Their dot product/product of lengths should yield cosine 30.
I got dw/dt = sqrt(3)w^2

Is that correct? Don't I also know that wt = (pi/2 - pi/6)? Couldn't I have calculated w using that?
 
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  • #2
hi peripatein! :smile:

(try using the X2 button just above the Reply box :wink:)
peripatein said:
a_tot = (-r*w^2,r*dw/dt)
a_tang = (0,r*dw/dt)
Their dot product/product of lengths should yield cosine 30.
I got dw/dt = sqrt(3)w^2

yes :smile:

but wouldn't it be easier to say that the ratio of the radial and tagential components must be tan30° ? :wink:
Don't I also know that wt = (pi/2 - pi/6)?

not following you :confused:
 

1. How do you calculate the angular acceleration of a wheel of radius R?

The angular acceleration of a wheel of radius R can be calculated using the formula α = a/R, where α represents the angular acceleration, a represents the total acceleration, and R represents the radius of the wheel.

2. What is the relationship between angular acceleration and total acceleration?

The angular acceleration and total acceleration are directly proportional, meaning that as the total acceleration increases, the angular acceleration also increases. This relationship is represented by the formula α = a/R.

3. How do you determine the total acceleration of a wheel given a vector of total acceleration?

To determine the total acceleration of a wheel given a vector of total acceleration, you can use the Pythagorean theorem. The total acceleration is equal to the square root of the sum of the squares of the x and y components of the vector.

4. Can the radius of a wheel affect its angular acceleration?

Yes, the radius of a wheel can affect its angular acceleration. A larger radius will result in a smaller angular acceleration, while a smaller radius will result in a larger angular acceleration.

5. What units are used to measure angular acceleration?

Angular acceleration is typically measured in radians per second squared (rad/s²), but it can also be measured in degrees per second squared (°/s²). Both units represent the change in angular velocity per unit time.

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