Along string is wrapped around a 6.6-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. the string is then pulled with a constant acceleration of 1.5 m/s2 until 1.3 m of string has been unwound. if the string unwinds without slipping, what is the cylinder's angular speed, in rpm, at this time?

Explanation:

It is given that,

Diameter of cylinder, d = 6.6 cm

Radius of cylinder, r = 3.3 cm = 0.033 m

Acceleration of the string,

Displacement, d = 1.3 m

The angular acceleration is given by :

The angular displacement is given by :

Using the third equation of rotational kinematics as :

Here,

Since, 1 rad/s = 9.54 rpm

So,

So, the angular speed of the cylinder is 571.42 rpm. Hence, this is the required solution.

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