Question 158: Motion in 2D & Vectors

Question

Let $$\omega_1, \omega_2$$ and $$\omega_3$$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $$x_1, x_2$$ and $$x_3$$ are their respective angular distances in 1 minute then the factor which remains constant $$(k)$$ is

Accepted Answer

$$\begin{aligned}
& \omega_1=\frac{2 \pi}{60} ; \quad x_1=\frac{2 \pi}{60} 	imes 60=2 \pi \\
& \omega_2=\frac{2 \pi}{3600} ; \quad x_2=\frac{2 \pi}{3600} 	imes 60=\frac{2 \pi}{60} \\
& \omega_3=\frac{2 \pi}{3600 	imes 12} ; \quad x_3=\frac{2 \pi}{3600 	imes 12} 	imes 60=\frac{2 \pi}{720} \\
& \frac{\omega_1}{x_1}=\frac{\omega_2}{x_2}=\frac{\omega_3}{x_3}=\frac{1}{60}=k
\end{aligned}$$

Answer

$$\frac{\omega_1}{x_1}=\frac{\omega_2}{x_2}=\frac{\omega_3}{x_3}=k$$

Answer

$$\omega_1 x_1=\omega_2 x_2=\omega_3 x_3=k$$

Answer

$$\omega_1 x_1^2=\omega_2 x_2^2=\omega_3 x_3^2=k$$

Answer

$$\omega_1^2 x_1=\omega_2^2 x_2=\omega_3^2 x_3=k$$

Motion in 2D & Vectors

Let $\omega_1, \omega_2 and \omega_3 be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If x_1, x_2 and x_3 are their respective angular distances in 1 minute then the factor which remains constant (k)$ is

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