Example 10.2 from College Physics, 10.1 Angular Acceleration

Calculating the Angular Acceleration of a Motorcycle Wheel

A powerful motorcycle can accelerate from 0 to 30.0 m/s (about 108 km/h) in 4.20 s. What is the angular acceleration of its 0.320-m-radius wheels? (See Figure 10.6.)

The figure shows the right side view of a man riding a motorcycle hence, depicting linear acceleration a of the motorcycle pointing toward the front of the bike as a horizontal arrow and the angular acceleration alpha of its wheels, shown here as curved arrows along the front of both the wheels pointing downward.

Figure 10.6 The linear acceleration of a motorcycle is accompanied by an angular acceleration of its wheels.

Strategy

We are given information about the linear velocities of the motorcycle. Thus, we can find its linear acceleration $a_{t}$ . Then, the expression $α = \frac{a_{t}}{r}$ can be used to find the angular acceleration.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The linear acceleration is
$\begin{array}{l} a_{t} & = & \frac{Δ v}{Δ t} \\ = & \frac{30.0 m/s}{4.20 s} \\ = & 7.14 {m/s}^{2} . \end{array}$
10.15

We also know the radius of the wheels. Entering the values for $a_{t}$ and $r$ into $α = \frac{a_{t}}{r}$ , we get
$\begin{array}{l} α & = & \frac{a_{t}}{r} \\ = & \frac{7.14 {m/s}^{2}}{0.320 m} \\ = & 22.3 {rad/s}^{2} . \end{array}$
10.16

Discussion

Units of radians are dimensionless and appear in any relationship between angular and linear quantities.

How did it go?

Solution

Solution