## Related questions with answers

Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s$^2$ , what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?

Solution

Verified$\textbf{Knowns}$

\normalsize We know that the rotational kinematic equation that describes the relationship among the final angular velocity $\color{#c34632}\omega$, the initial angular velocity $\color{#c34632}\omega_o$, time $\color{#c34632}t$ and the angular acceleration $\color{#c34632}\alpha$ is given by:

$\begin{gather*} \omega = \omega_o + \alpha t \tag{1} \end{gather*}$

We also know that the relation between the linear acceleration and the angular acceleration is given by:

$\begin{gather*} a = r\alpha\tag{\textbf{R.1}} \end{gather*}$

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