Question

Find angular speed of second's clock.

Answer 1

To find :

• Angular speed (ω) of seconds hand of a clock.

Solution :

• We know that,

        Angular speed (ω) = angle swept by radius vector(θ) ÷ time taken(t)

• Now, for one complete rotation, the seconds hand sweeps a total angle of 2π radians .
• ∴ θ = 2π
• For this, it takes a total of 1 minute i.e. 60 seconds.
• Hence the time period of the seconds hand of the clock is 60 seconds.
• ∴ t = 60
• Substituting the values of θ and t in the above equation :

        ω = 2π/60

     ∴ ω = π/30  radians/second

Answer 2

Hence the angular speed for second clock is ω = π / 30

Explanation:

• As we know that the second hand clock completes one round in a minute.
• The expression fir the complete sound of one clock = 2πrad
• Now for second clock the expression ca be written as:
• ω = 2πrad / min ( 1 minute / 60 second)
• ω = π / 30 rad / second

Hence the angular speed for second clock is ω = π / 30