Chapter 4, Problem 40RE

(a)

To determine

To Find: The number of revolutions per minute

Answer to Problem 40RE

  $Thenumberofrevolutionsperminute\approx 336.306$

Explanation of Solution

Given information: A car is moving at a rate of $28milesperhour$ and diameter of car is $\frac{7}{3}feet$

Concept used: If $\theta$ is the angle (in radian measure)corresponding to the arc length $s$, then the angular speed $\omega$

of the particle is

  $Angularspeed$

  $\omega =\frac{centralangle}{time}=\frac{\theta }{t}$

Calculation:

car is moving $=28milesperhour$

diameter of car $=\frac{7}{3}feet$

then radius $=r=\frac{diameter}{2}=\frac{7}{6}$

  $\because 1mile=5280feet$

  $\therefore 28miles=5280\times 28=147,840feet$

car is moving $=28miles$

  $\frac{miles}{hour}$

  $=\frac{5280\times 28}{60}=2464\frac{feet}{\min }$

Use the formula

  $\begin{array}{l}v=r\omega \\ \omega =\frac{v}{r}\\ \omega =\frac{2464}{\frac{7}{6}}\\ \omega =2112\frac{rad}{\min }\\ \because 1revolution=2\pi radian\\ \therefore \omega =2112\frac{rad}{\min }\times \frac{1}{2\pi }\\ \omega \approx 333.306\frac{rev}{\min }\end{array}$ .

(b)

To determine

To Find: The angular speed of the wheels

Answer to Problem 40RE

  $Theangularspeedofthewheels=2112\frac{rad}{\min }$

Explanation of Solution

Given information: A car is moving at a rate of 28 miles per hour and diameter of car is 7 3 feet

Concept used: : If $\theta$ is the angle (in radian measure)corresponding to the arc length $s$, then the angular speed $\omega$

of the particle is

  $Angularspeed$

  $\omega =\frac{centralangle}{time}=\frac{\theta }{t}$

Calculation:

car is moving $=28milesperhour$

diameter of car $=\frac{7}{3}feet$

then radius $=r=\frac{diameter}{2}=\frac{7}{6}$

  $\because 1mile=5280feet$

  $\therefore 28miles=5280\times 28=147,840feet$

car is moving $=28miles$

  $\frac{miles}{hour}$

  $=\frac{5280\times 28}{60}=2464\frac{feet}{\min }$

Use the formula

  $\begin{array}{l}v=r\omega \\ \omega =\frac{v}{r}\\ \omega =\frac{2464}{\frac{7}{6}}\\ \omega =2112\frac{rad}{\min }\end{array}$