Question

The second hand of a watch is 3.0cm long. find the linear speed of its tip . what will be the change in the velocity of its tip in covering one fourth of the circumference? what is covering one half of the circumference?

Answer 1

Angular speed = 2 pi radians/ 60 sec
w = pi/30 red/sec.

Linear speed = v = r w =
v = 3×pi/30= pi/10 cm/sec.

change in velocity after one quarter of minute:
$\sqrt{ {v}^{2} + {v}^{2} } = \sqrt{2} v = \sqrt{2} \frac{\pi}{30} cm {sec}^{ - 1}$

change i n velocity after half of circle:
2 v = pi/15 cm/sec.

Answer 2

Hey there,

The minute hand covers 360° in 60 seconds,
And 180°=π

So angular speed(ω)=
2π/60 seconds

Since linear speed v=rω
So,
v=3*π/30=π/10 cm/s

According to law of linear vectors--
Δv=√(v²+u²)*cos90°                     [FOR A QUARTER CIRCLE]
But linear velocity is always same, so v=u

Δv=v√2

=π√2/10 cm/s

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