Question

A string is wound around a wheel of radius 20 cm. How large is the angle through which the wheel must turn to unwind 30 cm of the string?

Answer 1

Answer on Question 55317, Physics, Mechanics | Kinematics | Dynamics

Question:

A string is wound around a wheel of radius $20\mathrm{cm}$. How large is the angle through which the wheel must turn to unwind $30\mathrm{cm}$ of the string?

Solution:

We can find the angle $\theta$ through which the wheel must turn to unwind $30\mathrm{cm}$ of the string from the relation between linear and angular variables:

$$s = \theta r,$$

here, $s$ is the length of the string unwound, $r$ is the radius of the wheel.

From this formula we can find the angle $\theta$:

$$\theta = \frac{s}{r} = \frac{0.3\mathrm{m}}{0.2\mathrm{m}} = 1.5\mathrm{rad}.$$

Answer:

$$\theta = 1.5\mathrm{rad}.$$

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