Question

What is the angular displacement of the second hand on a clock after 59 seconds?

Answer 1

The angular displacement of the second hand on a clock after 59 second is -6.17 rad.

Answer: Option A

Explanation:

As we know angular displacement is defined as the change in the displacement in a circular motion for a given angle. So, angular displacement is derived using the formula

       $\text { Angular Displacement }=\frac{\text { Total displacement }}{\text { Radius of the circular path }}$

Also, in a clock the second hand travel a distance of 2π in 1 minute. If for 60 s, the angular displacement is 2π. Then for 1 s, the angular displacement will be

           $\text { Angular Displacement for } 1 s=\frac{2 \pi}{60}$

And for 59 seconds, the angular displacement will be

          $\text { Angular Displacement for } 59 s=\frac{2 \pi}{60} \times 59 \text { rad }$

As we do not know the displacement of seconds hand after 59 seconds but the angular displacement will be having a negative sign as the clock hands move in clockwise direction.  So ,

         $\text { Angular Displacement for } 59 s=-\frac{2 \times 3.14 \times 59}{60}=-6.17 \mathrm{rad}$

Answer 2

Answer:

a. -6.17 rad

Explanation:

60 seconds is 2π radians.  Writing a proportion:

2π / 60 = x / 59

x = 6.17

The displacement is negative because the second hand moves clockwise.