Question

What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π.

Answer 1

The circle is 12 foot diameter.
Circumference = (pi)(12) = 37.70 feet
14.13/37.70 = 0.3748
0.3748(360 degrees) = 134.9 degrees
134.9degrees/3sec = 45degrees/second

Answer 2

Angular velocity=0.785rad/s

Explanation:

Let us first consider the circumference of pendulum that is:

Circumference=
`2{\pi}r`, where r is the radius.

Now, it is given that the radius is= 6 foot , therefore

Circumference=
`2{*}3.14{*}6`

Circumference=
`37.68foot`

Now, Calculate enough time to produce a whole circular, by causing a proportion with both ratios:

Ratio 1 =
`(x)/(37.68)` and Ratio 2=
`{(3)/(14.13)}`

Thus, ratio 1 = ratio 2

`(x)/(37.68)={(3)/(14.13)}`

`x=\frac{3{*}37.68}{14.13}`

`x=8s`

Also, Calculate the angular speed as the
`2\pi`radian (which is the full total angle of the group) divided by enough time.

So the angular speed is =
`(2\pi rad)/(8s)=\frac{2{*}3.14 rad}{8s}=0.785rad/s`.