Question

The difference between angular speed of minute hand and second hand of a clock is:
A ${\displaystyle \frac{59\pi }{900}}$ rad $/$ s
$\mathrm{B}{\displaystyle \frac{59\pi }{1800}}\mathrm{rad}/\mathrm{s}$
$\mathrm{C}{\displaystyle \frac{59\pi }{24000}}\mathrm{rad}/\mathrm{s}$
D ${\displaystyle \frac{59\pi }{3600}}$ rad $/$ s

Answer 1

Hint: We should know that velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance which is a scalar quantity per time ratio. On the other hand, velocity is a vector quantity; it is direction-aware. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion in this case. Based on this we have to solve this question.

Complete step by step answer
We know that angular Velocity determines how fast or how slow an object is rotating. Or one can say that angular velocity is the rate change of angular displacement. The S.I Unit of angular displacement is radians per seconds. Or the S.I Unit of angular velocity is rpm which means revolution per minute. The SI unit of angular velocity is expressed as radians per second with the radian having a dimensionless value of unity, thus the SI units of angular velocity are listed as 1/s. Angular velocity is usually represented by the symbol omega
At first let us begin with time taken by the second hand to complete one complete rotation is 60 seconds.
Thus, the angular velocity of second hand ${\mathrm{w}}_{\mathrm{s}}={\displaystyle \frac{2\pi }{60}}\mathrm{rad}/\mathrm{s}$
So, the time taken by the minute hand to complete one complete rotation is 3600 seconds.
Thus, angular velocity of minute hand ${\mathrm{w}}_{\mathrm{m}}={\displaystyle \frac{2\pi }{3600}}\mathrm{rad}/\mathrm{s}$
Difference in angular velocity ${\mathrm{w}}_{\mathrm{s}}-{\mathrm{w}}_{\mathrm{m}}={\displaystyle \frac{2\pi }{60}}-{\displaystyle \frac{2\pi }{3600}}$
$\Rightarrow {\text{w}}_{\text{s}}-{\text{w}}_{\text{m}}={\displaystyle \frac{59\pi }{1800}}\text{rad}/\text{s}$

So, the correct option is option B.

Note: We should know that if an object's speed or velocity is increasing at a constant rate then we say it has uniform acceleration. The rate of acceleration is constant. If a car speeds up then slows down then speeds up it doesn't have uniform acceleration. The instantaneous acceleration, or simply acceleration, is defined as the limit of the average acceleration when the interval of time considered approaches 0. It is also defined in a similar manner as the derivative of velocity with respect to time. If an object begins acceleration from rest or a standstill, its initial time is 0. If we get a negative value for acceleration, it means the object is slowing down. The acceleration of an object is its change in velocity over an increment of time. This can mean a change in the object's speed or direction. Average acceleration is the change of velocity over a period of time. Constant or uniform acceleration is when the velocity changes the same amount in every equal time period.