Chapter 8.1, Problem 1PP

a.

To determine

Angular displacement of second hand.

Answer to Problem 1PP

  $120\pi \text{ radian}$

Explanation of Solution

Time is given t = 1 hour

In one complete revolution total angular displacement by any hand is $2\pi$ radian.

Second hand completes 60 revolution in 1 hour.

Therefore, angular displacement of second hand is:

  $\begin{array}{l}\theta =60\times 2\pi \\ =120\pi \text{ radian}\end{array}$

b.

To determine

Angular displacement of minute hand.

Answer to Problem 1PP

Angular displacement of minute hand is $2\pi \text{ radian}$ .

Explanation of Solution

Time is given t = 1 hour

In one complete revolution total angular displacement by any hand is $2\pi$ radian.

Minute hand completes 1 revolution in 1 hour.

Therefore, angular displacement of minute hand is:

  $\begin{array}{l}\theta =1\times 2\pi \\ =2\pi \text{ radian}\end{array}$

c.

To determine

Angular displacement of hour hand.

Answer to Problem 1PP

Angular displacement of hour hand is $\frac{\pi }{6}\text{ radian}$

Explanation of Solution

Time is given t = 1 hour

In one complete revolution total angular displacement by any hand is $2\pi$ radian.

Hour hand completes 1 revolution in 12 hours.

So, number of revolutions in 1 hour is $\frac{1}{12}$

Therefore, angular displacement of hour hand is:

  $\begin{array}{l}\theta =\frac{1}{12}\times 2\pi \\ =\frac{\pi }{6}\text{ radian}\end{array}$