A horizontal spring has one end firmly attached to a wall and the other end attached to a mass. The mass can slide freely on a s
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Answer:
Explanation:
Angular acceleration is defined by
Angular velocity is related to the period by
Putting all together:
Taking our initial (i) point now and our final (f) point one year later, we would have:
So for our values we have:
Where the minus sign indicates it is decelerating.
We know that arc length (x(t)) is given with the following formula:
Where r is the radius of the barrel. We must keep in mind that as barrel rolls its radius decreases because less and less tape is left on it.
If we say that the thickness of the tape is D then with every full circle our radius shrinks by d. We can write this down mathematically:
When we plug this back into the first equation we get:
We must solve this quadratic equation.
The final solution is:
It is rather complicated solution. If we asume that the tape has no thickness we get simply:
Where r is the radius of the barrel. We must keep in mind that as barrel rolls its radius decreases because less and less tape is left on it.
If we say that the thickness of the tape is D then with every full circle our radius shrinks by d. We can write this down mathematically:
When we plug this back into the first equation we get:
We must solve this quadratic equation.
The final solution is:
It is rather complicated solution. If we asume that the tape has no thickness we get simply: