Chapter 8.1, Problem 7SSC

a.

To determine

Angular displacement of an hour hand.

Answer to Problem 7SSC

Angular displacement is $\theta =\frac{\pi }{4}\text{ radian}$

Explanation of Solution

Given :

Time, $t=2\text{ hour}$

Formula used :

  $1\text{ rev = 2}\pi \text{ radian}$

Calculation :

An hour hand complete one revolution in 12 hour.

Therefore, angular displacement in 12 hour is $2\pi \text{ radian}$

So angular displacement is 2 hour is ;

  $\frac{2}{12}\times 2\pi =\frac{\pi }{4}\text{ radian}$

Conclusion :

Therefore, angular displacement of hour hand in 2 hour is $\frac{\pi }{4}\text{ radian}$ .

b.

To determine

Angular displacement of the minute hand.

Answer to Problem 7SSC

Angular displacement is $4\pi \text{ radian}$

Explanation of Solution

Given :

Time, $t=2\text{ hour}$

Formula used :

  $1\text{ rev = 2}\pi \text{ radian}$

Calculation :

An hour minute complete one revolution in 1 hour.

Therefore, angular displacement in 1 hour is $2\pi \text{ radian}$

So angular displacement is 2 hour is ;

  $\begin{array}{l}\theta =2\times 2\pi \\ =4\pi \text{ radian}\end{array}$

Conclusion :

Therefore, angular displacement of minute hand in 2 hour is $4\pi \text{ radian}$ .

c.

To determine

Angular displacement of the second hand.

Answer to Problem 7SSC

Angular displacement is $\theta =240\pi \text{ radian}$

Explanation of Solution

Given :

Time, $t=2\text{ hour}$

Formula used :

  $1\text{ rev = 2}\pi \text{ radian}$

Calculation :

A second hand completes 60 revolution 1 hour

Therefore, angular displacement in 1 hour is $120\pi$

So angular displacement is 2 hour is ;

  $\begin{array}{l}\theta =2\times 120\pi \\ =240\pi \text{ radian}\end{array}$

Conclusion :

Therefore, angular displacement of second hand in 2 hour is $240\pi \text{ radian}$ .