Chapter 11.7, Problem 34PPS

(a)

To determine

To write: a formula describing the speed of a spinning object.

Answer to Problem 34PPS

The speed of the spinning object is $\left[v=\frac{2\pi r}{T}\right]$

Explanation of Solution

Calculation:

The objective is to write a formula describing the speed of a spinning object.

The speed of a spinning object is as follows.

  $v=\frac{2\pi r}{T}$

Therefore, the speed of the spinning object is $\left[v=\frac{2\pi r}{T}\right]$

Conclusion:

Therefore, the speed of the spinning object is $\left[v=\frac{2\pi r}{T}\right]$

(b)

To determine

To find: the speed in miles per hour.

Answer to Problem 34PPS

Therefore, the speed is [219.8] inches/second

Explanation of Solution

Given:

The radius is $3\frac{1}{2}$ inches.

Tire makes one revolution in every $\frac{1}{10}$ second.

Calculation:

The radius is $3\frac{1}{2}$ inches.

Tire makes one revolution in every $\frac{1}{10}$ second.

The objective is to find the speed in miles per hour.

The speed is calculated below.

  $v=\frac{2\pi r}{T}=\frac{2\pi \left(3\frac{1}{2}\right)}{\frac{1}{10}}=219.8$

Therefore, the speed is [219.8] inches/second

Conclusion:

Therefore, the speed is [219.8] inches/second