Chapter 8.1, Problem 3PP

To determine

The diameter of the truck’s wheels.

Answer to Problem 3PP

  $0.706\text{m}$

Explanation of Solution

Given:

Linear acceleration of the truck is $1.85{\text{m/s}}^{\text{2}}$ .

Angular acceleration of the wheels of the truck is $5.23{\text{rad/s}}^{\text{2}}$ .

Formula used:

For a rotating a rigid object, its linear acceleration( a ) can be related to its angular acceleration $\left(\alpha \right)$ as:

  $a=r\alpha$

Where, r is the radius of the object.

Calculation:

Now the linear and angular acceleration of the wheels of the truck is given, then the radius of the wheels will be:a

  $\begin{array}{c}r=\frac{a}{\alpha }\\ =\frac{1.85}{5.23}\\ =0.353\text{}\text{m}\end{array}$

Then, the diameter of the wheels of the truck is,

  $\begin{array}{c}d=2r\\ =2\left(0.353\right)\text{}\text{m}\\ \text{= 0}\text{.706 m}\end{array}$

Conclusion:

Thus, the diameter of the wheels of the truck is $0.706\text{m}$ .