Can I use this solution? Angular motion

In summary, the wheel starts from rest and accelerates at a constant rate of 3 rad/s^2. In a certain 4 second interval, it turns through 120 radians. The time it takes to reach this interval is not the same as the time it takes to turn 120 radians from the starting point. To find the time it takes to reach this interval, two equations are needed. The first equation is Δθ = ω0⋅t + ½αt^2, and the second equation is Δθ = ωf⋅t - ½αt^2. Solving for t, it can be found that the time it takes to reach the 4 second interval is
  • #1
OrlandoLewis
25
1

Homework Statement


Starting from rest, a wheel has constant α = 3.0 rad/s2. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval?

ω0 = 0
α = 3.0 rad/s2
θf = 120 rad

Homework Equations


Δθ = ω0⋅t + ½αt2

The Attempt at a Solution


120 rad = (1/2)(3.0 rad/s2)(t2)
Solving for t:
t = [2(120 rad) / (3.0 rad/s^2)]½
t = 8.49 s
Subtracting 4.0 s to the said time leads to my final answer, 4.9 s

The book says that the answer should be 8.0 s.
 
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  • #2
It says "during a certain 4.0s interval " it could be between any time interval.Your equation describes us what is the time when it makes 120 rad we are not looking for that,we are looking for a time interval which object makes 120 rad.
Can you see the difference ?
 
  • #3
During the given interval, Δθ = 120 rad. But that's not measured from the starting point.

You found the time it takes to go from the starting point to θf = 120 rad, which is a different problem.

Set up two equations.

Edit: Oops, didn't see that Arman777 just said the same thing. :-)
 
  • #4
Arman777 said:
It says "during a certain 4.0s interval " it could be between any time interval.Your equation describes us what is the time when it makes 120 rad we are not looking for that,we are looking for a time interval which object makes 120 rad.
Can you see the difference ?
It's still pretty vague to me from how you said it. So I'll try to explain as far as I can understand.

At the beginnig it starts to accelerate up to a certain velocity. From that point up to 4 seconds, the said theta is measured until 210 radians.
Is that how I should interpret the problem?
 
  • #5
OrlandoLewis said:
It's still pretty vague to me from how you said it. So I'll try to explain as far as I can understand.

At the beginnig it starts to accelerate up to a certain velocity. From that point up to 4 seconds, the said theta is measured until 210 radians.
Is that how I should interpret the problem?

It made some rad ##θ_1## between ##t=0## and ##t_1##,
After 4 sec, which let's call is ##t_2## (or ##t_1+4##) it makes ##θ_2## rad (between ##t_2## and ##t=0##)
In between those time intervals (##t_2## and ##t_1##) it makes ##120## rad.
 
  • #6
Arman777 said:
It made some rad ##θ_1## between ##t=0## and ##t_1##,
After 4 sec, which let's call is ##t_2## (or ##t_1+4##) it makes ##θ_2## rad (between ##t_2## and ##t=0##)
In between those time intervals (##t_2## and ##t_1##) it makes ##120## rad.
Yes, but I feel it could be expressed yet more clearly.
It accelerates at 3 rad s-2 from rest for some time t, turning through some angle in the process. Continuing with the same acceleration for another 4 seconds it turns through a further 120 radians. Find t.
 

Related to Can I use this solution? Angular motion

1. Can I use this solution for all types of angular motion?

Yes, this solution can be applied to any type of angular motion, including rotational motion, simple harmonic motion, and circular motion.

2. Do I need any special equipment to use this solution?

No, this solution can be used with basic equipment such as a protractor, ruler, and stopwatch. However, more precise measurements may require specialized equipment.

3. How accurate is this solution?

The accuracy of this solution depends on the accuracy of the measurements taken and the assumptions made in the calculations. It is important to use precise equipment and make accurate measurements for the most accurate results.

4. Can this solution be used for both uniform and non-uniform angular motion?

Yes, this solution can be used for both uniform and non-uniform angular motion. However, some adjustments may need to be made for non-uniform motion, such as accounting for changes in angular velocity.

5. Are there any limitations to using this solution?

While this solution is applicable to a wide range of angular motion problems, it may not be suitable for more complex situations such as those involving friction or air resistance. In these cases, more advanced solutions may be necessary.

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