Question

If the length of the second's hand in a stop clock is 3 cm, the angular velocity and linear velocity of the tip is:

Answer 1

Given,

length of minute hand 3cm which is also radius of circular path of second hand.

r = 3

We know that angular velocity

$\\ \\ \omega = \frac{Angle}{Time} \\ \\ \omega = \frac{2\pi}{60\sec} \\ \\ \omega = \frac{\pi}{30} Radian/sec \\ \\ \text{We know that linear velocity,} \\ \\ v = r\omega \\ \\ v = 3* \frac{\pi}{30} cm/sec \\ \\ \textbf{v = 0.314 \ cm/sec}$

Answer 2

Hey mate,

◆ Answer-
ω = 0.1047 rad/s
v = 3.141×10^-3 m/s


◆ Explanation-
# Given-
r = 3 cm = 0.03 m

# Solution-
Time period of second hand is 1 min. i.e. T = 60 s

Angular velocity is calculated by-
ω = 2π/T
ω = 2π/60
ω = 0.1047 rad/s

Linear velocity of the tip is calculated by-
v = rω
v = 0.03 × 0.1047
v = 3.141×10^-3 m/s

Therefore, angular velocity of second hand is 0.1047 rad/s and linear velocity of tip is 3.141×10^-3 m/s.

Hope this helps..