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

Step-by-step explanation:

Given

Initial linear speed
`v_1=8 m/s`

initial angular velocity
`\omega _1=(v_1)/(r)=(8)/(0.6)=13.33 rad/s`

Speed after 4.1 s is
`v_2=2.2 m/s`

`\omega _2=(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+(\alpha t^2)/(2)`

`\theta =13.33* 4.1-(2.37\cdot 4.1^2)/(2)`

`\theta =54.66-19.75`

`\theta =34.91 rad`