Question

Calculate the angular speed and linear speed
of the tip of a minute hand of length 10 cm.​

Answer 1

$\rule{200}{2}$

$\huge\boxed{\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R:-}}}}}$

Data : The minute hand completes one rotation in one hour. Hence, its period is

T= 1 hour = 60 min = 60 x 60 s = 3600 s

... Its angular speed is

$w = \frac{2\pi}{t} \\ \\ = \frac{2 \times 3.142}{3600} \\ \\ = 1.746 \times {10}^{ - 3} rad$

1.746 ✖️ 10^-4 m/s

As the minute hand rotates, its tip revolves along a circle of radius 10 cm.

...r = 10 cm = 0.1 m

Hence, its linear speed is

$v = wr = 1.746 \times {10}^{ - 3} \times .0.1$

= $\01 .746 x {10}^{-4}m/s$

$\rule{200}{2}$

Answer 2

Explanation:

Data : The minute hand completes one rotation in one hour. Hence, its period is

T= 1 hour = 60 min = 60 x 60 s = 3600 s

... Its angular speed is

\begin{lgathered}w = \frac{2\pi}{t} \\ \\ = \frac{2 \times 3.142}{3600} \\ \\ = 1.746 \times {10}^{ - 3} rad\end{lgathered}

w=

t

2π

=

3600

2×3.142

=1.746×10

−3

rad

\boxed{\boxed{1.746 x 10^-4 m/s}}

1.746x10

−

4m/s

As the minute hand rotates, its tip revolves

along a circle of radius 10 cm.

...r = 10 cm = 0.1 m

Hence, its linear speed is

v = wr = 1.746 \times {10}^{ - 3} \times .0.1v=wr=1.746×10

−3

×.0.1

=