Question

What is the angular speed of the second hand of a clock? If the second hand is $10cm$ long, then find the linear speed of its tip. (in $rad/s$ and $m/s$)

• A. $0.1047,0.01047$
  
• B. $1047,0.01047$
  
• C. $0.1047,1047$
  
• D. $0.0047,0.01047$
  

Answer 1

The correct option is A $0.1047,0.01047$

Angular speed is the rate at which an object changes its angle in radians, in a given time period.

Angular speed $\omega$= $\frac{angulardisplacement}{time}$= $\frac{\theta }{t}$

In one complete rotation, second hand cover 2$\pi$ rad of angular displacment in 60 seconds.

Angular speed $\omega$= $\frac{\left(\theta \right)}{t}$ = $\frac{2\pi }{60}$ $=0.1047$ $rad/s$

Speed of linear Tip $v=$ radius$\times$ angular speed

$v=$ $0.1m\times 0.1047$ = $0.01047m/s$

Hence Option (A) is correct.