Question

A long string is wrapped around a 6.0-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of 1.9 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?

Answer 1

Question #62150, Physics – Mechanics | Relativity

A long string is wrapped around a 6.0-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of $1.9 \, \text{m/s}^2$ 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?

Solution

The final linear speed of the string:

$$v^2 = 2ad;$$ $$v = \sqrt{2 \times 1.9 \times 1.3} = 2.22 \, \text{m/s};$$

The angular speed is:

$$\omega = \frac{v}{r} = \frac{2.22}{0.06} = 37 \, \text{rad/s}$$

Answer: 37 rad/s.

https://www.AssignmentExpert.com