Question

A motorcycle, which has an initial linear speed of 8.0 m/s, decelerates to a speed of 2.2 m/s in 4.1 s. Each wheel has a radius of 0.60 m and is rotating in a counterclockwise (positive) directions. What is
(a) the constant angular acceleration (in rad/s2) and
(b) the angular displacement (in rad) of each wheel?

Answer 1

Answer:

Explanation:

Given

Initial linear speed $v_1=8 m/s$

initial angular velocity $\omega _1=\frac{v_1}{r}=\frac{8}{0.6}=13.33 rad/s$

Speed after 4.1 s is  $v_2=2.2 m/s$

$\omega _2=\frac{2.2}{0.6}=3.66 rad/s$

using $\omega _2=\omega _1+\alpha t$

where $\alpha$is angular acceleration

$3.66=13.33+\alpha \cdot 4.1$

$\alpha =-2.37 rad/s^2$ i.e. clockwise

(b)angular displacement

$\theta =\omega _1t+\frac{\alpha t^2}{2}$

$\theta =13.33\times 4.1-\frac{2.37\cdot 4.1^2}{2}$

$\theta =54.66-19.75$

$\theta =34.91 rad$