Question

A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 66 cm and is wound around the top at a spot where its radius is 1.7 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +9 rad/s2. What is the final angular velocity of the top when the string is completely unwound?

Answer 1

Answer:

$\omega_f=26.43\frac{rad}{s}$

Explanation:

Arc length of the circle is the measure of the distance between two points along the circumference, is given by:

$s=r\theta$

Solving for $\theta$ and replacing the given values:

$\theta=\frac{s}{r}\\\theta=\frac{66cm}{1.7cm}\\\theta=38.82rad$

Now, we use a rotational kinematics formula in order to calculate the final angular velocity. Since the top is initially at rest $\omega_0=0$:

$\omega_f^2=\omega_0^2+2\alpha\theta\\\omega_f^2=2(9\frac{rad}{s^2})(38.82rad)\\\omega_f=\sqrt{698.76\frac{rad^2}{s^2}}\\\omega_f=26.43\frac{rad}{s}$