Suppose a yo-yo has a center shaft that has a 2.70 cm radius and that its string is being pulled. If the string is stationary and the yo-yo accelerates away from it at a rate of 1.65 m/s2, what is the angular acceleration of the yo-yo

Explanation:

For this case we can use the following formula for the angular velocity:

where represent the final angular velocity , the initial angular velocity , t the time and the angular acceleration.

And for the linear acceleration we have this formula:

Where a represent the linear acceleration and the angular acceleration.

For this case the linear acceeleration is given

And the radius of the yo-yo is also given

So then we can use the following formula:

If we replace the values we got:

And solving for we got: