# Can I use this solution? Angular motion

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1. Feb 11, 2017

### OrlandoLewis

1. The problem statement, all variables and given/known data
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

2. Relevant equations
Δθ = ω0⋅t + ½αt2

3. The attempt at a solution
Solving for t:
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.

2. Feb 11, 2017

### Arman777

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 differance ?

3. Feb 11, 2017

### Staff: Mentor

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. Feb 11, 2017

### OrlandoLewis

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. Feb 11, 2017

### Arman777

It made some rad $θ_1$ between $t=0$ and $t_1$,
After 4 sec, which lets 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. Feb 11, 2017

### haruspex

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.