# Math Help - i need help w/ linear/angular speed

1. ## i need help w/ linear/angular speed

An object is traveling around a circle with a radius of 10 cm. If in 20s a central angle of 1/3 radians is swept out, what is the linear speed of the object?

2. Originally Posted by tangerine_tomato
An object is traveling around a circle with a radius of 10 cm. If in 20s a central angle of 1/3 radians is swept out, what is the linear speed of the object?
You can do this in two ways.
1. v = d / t
The distance traveled is the arc length swept out. So d = (10 cm)(1/3 rad) = 10/3 cm. This is covered in 20 s, so
$v = \frac{d}{t} = \frac{\frac{10}{3}~cm}{20~s} = \frac{1}{6}~cm/s$

2. Find the angular speed from $omega = \theta / t$ then find the linear speed by $v = r \omega$. It comes out to be the same thing in the end.

-Dan

3. Originally Posted by topsquark
You can do this in two ways.
1. v = d / t
The distance traveled is the arc length swept out. So d = (10 cm)(1/3 rad) = 10/3 cm. This is covered in 20 s, so
$v = \frac{d}{t} = \frac{\frac{10}{3}~cm}{20~s} = \frac{1}{6}~cm/s$

2. Find the angular speed from $omega = \theta / t$ then find the linear speed by $v = r \omega$. It comes out to be the same thing in the end.

-Dan
i dont understand how you find 10/3 for D

4. Originally Posted by tangerine_tomato
i dont understand how you find 10/3 for D
The arc length s (I used "d" here) is defined by $s = r \theta$ where $\theta$ is the central angle measured in radians.

-Dan