Question

A stone whirled at the end of the a rope 30cm long, makes 10 complete resolution in 2 seconds Find: A. The angular velocity in radians b. the linear speed c. the distance covered in 5 seconds​

Answer 1

Answers:

A: Angular velocity $\omega=31.40 \frac{r a d}{s}$

B: Linear velocity $v=9.42 \frac{m}{s}$

C: Linear Distance $d=47.1 \mathrm{m}$

Given:

Radius of the rope r=30cm=0.3m

Angular distance$\Delta \theta$=10 revolutions

Time taken t=2seconds

To find:

A: Angular velocity in radians

B: Linear speed

C: Distance covered in 5 seconds

Step by Step Explanations:

Solution:

A: Angular velocity in radians;

According to the formula, Angular velocity can be calculated as

Angular Velocity = angular distance/ time

$\omega=\Delta \theta / \Delta t$

Where $\omega$=Angular velocity

$\Delta \theta$=Angular distance=10 revolutions

Changing revolutions to radians multiply with $2 \pi$, so that we get

$=10 \times 2 \pi$

$=10 \times 2(3.14)$  

=62.80 rad/rev

$\Delta t$ =Change in time

Substitute the known values in the above equation we get

$\omega$=62.80 / 2  

$\omega=31.40 \frac{r a d}{s}$

B. Linear speed of the rope;

As per the formula

Linear speed = angular speed × radius

$v=\omega \times r$  

Where $\omega$=Angular velocity

v=Linear speed of the rope

r=Radius of the rope

Substitute the known values in the above equation we get

$v=31.40 \times 0.30$

$v=9.42 \frac{m}{s}$

C. Dsitance covered in 5 seconds;

Linear distance = linear speed × time

$d=v \times t$

Where d= Linear distance of the rope

v=Linear speed of the rope

t=Time taken

Substitute the known values in the above equation we get

$d=9.42 \times 5$

$d=47.1 \mathrm{m}$

Result:

Thus A: Angular velocity of the rope $\omega=31.40 \frac{r a d}{s}$

B Linear speed of the rope $v=9.42 \frac{m}{s}$

C: Distance covered in 5 seconds $d=47.1 \mathrm{m}$