Answer:
Around 73 revolutions
Explanation:
Tangential acceleration = Angular acceleration x radius
The tangential acceleration is the final speed divided by the time as it was initially at rest and therefore it gives a value of approximately 3.74 m/s^2. The angular acceleration becomes 12.46 rad/s^2 as of the above formula (remember to change the unit of the radius to meters).
Finally, to find the angular displacement we use the rotational equivalent of one of the equations used for uniformly accelerated rectilinear motion. i.e.
[tex]x \: = \frac{1}{2}at {}^{2} [/tex]
We use the angular displacement in place of x and angular acceleration in place of a to get an angular displacement of 460.8 rad or 73.3 revolutions.
