Physics.p: a stone whirled at the end of a rope 30cm long makes 10 complete in 2seconds find the angular velocity the lnear speed the distance covered in 5seconds

angular velocity=10*2PI/2 rad/sec

distance=angularveloicty*radius*time
= 10*2PI/2*.30*5 meters

Please calutate it for me how to get the answer

Please the answer

To find the angular velocity, linear speed, and distance covered, we'll use the following formulas:

1. Angular velocity (ω) = 2π × Number of revolutions / Time taken
2. Linear speed (v) = ω × Radius
3. Distance covered (s) = Linear speed × Time taken

Given:
- Length of the rope (radius) = 30 cm = 0.3 m
- Number of complete revolutions = 10
- Time taken = 2 seconds
- Time taken to find distance covered = 5 seconds

Now, let's calculate each value step by step:

1. Angular velocity (ω):
The number of complete revolutions is given as 10, and the time taken is given as 2 seconds. Using the formula, we have:
ω = 2π × Number of revolutions / Time taken
= 2π × 10 / 2
= 10π rad/s

So, the angular velocity is 10π rad/s.

2. Linear speed (v):
The radius is given as 0.3 m, and we already found the angular velocity as 10π rad/s. Using the formula, we have:
v = ω × Radius
= 10π × 0.3
= 3π m/s (approximately 9.42 m/s)

So, the linear speed is 3π m/s (approximately 9.42 m/s).

3. Distance covered (s):
To find the distance covered in 5 seconds, we'll use the linear speed v = 3π m/s calculated in the previous step. Using the formula, we have:
Distance covered = Linear speed × Time taken
= 3π × 5
= 15π m (approximately 47.12 m)

So, the distance covered in 5 seconds is 15π m (approximately 47.12 m).

In summary:
- The angular velocity is 10π rad/s.
- The linear speed is approximately 9.42 m/s.
- The distance covered in 5 seconds is approximately 47.12 m.