# THE YO-YO: A quantitative yo-yo consists of a disk (or other shape) fixed to an axle that has two strings wrapped around it. As the axle rolls off the strings: If the disk is rotating faster...

THE YO-YO: A quantitative yo-yo consists of a disk (or other shape) fixed to an axle that has two strings wrapped around it. As the axle rolls off the strings: If the disk is rotating faster and faster with a constant angular acceleration and takes 25 s to fall through the distance d = 30 cm from rest, what is the magnitude of its angular acceleration a? The radius of the disk is 5 mm.

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### 1 Answer

A quantitative yo-yo consists of a disk (or other shape) fixed to an axle that has two strings wrapped around it. As the disk falls, the string wrapped around it is unwrapped. The disk has a radius of 5 mm and drops 30 cm from rest. It takes 25 seconds to do this.

If the magnitude of angular acceleration of the disk is a, the relation s = u*t + (1/2)*a*t^2 can be used where s is the rotational motion of the disk.

Here, the circumference of the disk is `2*pi*0.5` cm. To fall 30 cm it has to rotate through `(30/(2*pi*0.5))*2*pi` radians.

`(30/(2*pi*0.5))*2*pi = 0*25 + (1/2)*a*25^2`

=> `60 = (1/2)*a*25^2`

=> `a = 120/25^2`

=> a = 0.192 rad/s^2

The constant angular acceleration of the disk is 0.192 rad/s^2