Starting from rest, a particle is constrained to move in a circle of radius 4 m. The tangential acceleration is a_t = 9 m/s^2. How long will it take to rotate 45º?

1 Answer
Paul N.
Mar 1, 2017

t = sqrt((2 pi)/9) "seconds"

Explanation:

If you think of this as a linear problem, the magnitude of the velocity will simply be:
|v| = |v_0| +|a*t|
And the other equations of motion work in a similar way:
d = v_0*t + 1/2 a*t^2

The distance along the direction of travel is simply one eighth of a circle:
d = 2 pi*r/8 = 2 pi * 4/8 = pi " meters"

Replacing this value in the equation of motion for distance gives:
pi = v_0*t + 1/2 a*t^2
pi = 0*t + 1/2 a*t^2
2 pi = a*t^2
2 pi = 9 * t^2
(2 pi)/9 = t^2
sqrt((2 pi)/9) = t

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