Question

What is Aangular Speed of the the following different hands of a watch
1. Second Hand
2. Minute hand
3. Hour watch​

Answer 1

Explanation:

We know that

$\boxed{Angular \: Speed \: (W) = \frac{2\pi \: n}{time}}$

1. For Second Hand

$= > W = \frac{2\pi \times 1}{60} \\ = > W = \frac{ \cancel2\pi}{ \cancel60} \\ = > \boxed{\ W = \frac{\pi}{30}\: rad/sec }$

2. For Minute Hand

$= > W = \frac{2\pi \times 1}{60 \times 60} \\ = > W = \frac{ \cancel2\pi}{ \cancel60 \times 60} \\ = > \boxed{W = \frac{\pi}{1800} \: rad/sec}$

3. For Hour Hand

$= > W = \frac{2\pi \times 1}{12 \times 60 \times 60} \\ = > W = \frac{ \cancel2\pi}{ \cancel12 \times 60 \times 60} \\ = > W = \frac{\pi}{6 \times 60 \times 60} \\ = > \boxed{W = \frac{\pi}{21600} \: rad/sec}$

Note- It's SI unit is rad/sec so time must to be in seconds while solving those type of numericals.

Answer 2

Answer :

1) Angular speed of second hand = 0.1046 rad/s

2) Angular speed of minute hand = 0.00174 rad/s

3) Angular speed of hour hand = 0.00014 rad/s

Explanation :

Formula :

Angular speed = 2π/T

1) Second hand

time (T1) = 60 sec

Angular speed of second hand = 2π/T1

= 2π/60

= π/30 rad/s

= 3.14/30

= 0.1046 rad/s

2) Minute hand

time (T2) = 60 min = 60×60 s = 3600 s

Angular speed of minute hand = 2π/T2

= 2π/3600

= π/1800 rad/s

= 3.14/1800

= 0.00174 rad/s

3) Hour hand

time (T3) = 12 × 60 × 60 sec = 43200 s

Angular speed of hour hand = 2π/T3

= 2π/43200

= π/21600 rad/s

= 3.14/21600

= 0.00014 rad/s

Note :

S.I. unit of angular speed is rad/s . So, time must be in seconds while solving a numerical.....