Question

A motorcyclist is traveling along a road and accelerates for 3.3 s to pass another car. The angular acceleration of each wheel is +1.8 rad/s2, and just after passing, the angular velocity of each wheel is + 74.1 rad/s, where the plus signs indicate counterclockwise directions. What is the angular displacement of each wheel during this time?

Answer 1

Angular displacement will be 234.729 radian

Step-by-step explanation:

We have given that time t = 3.3 sec

Angular acceleration
`\alpha =1.8rad/sec^2`

Final angular velocity
`\omega _f=74.1rad/sec`

From first equation of motion we know that
`\omega _f=\omega _i+\alpha t`

`\omega _i=\omega _f-\alpha t=74.1-3.3* 1.8=74.1-5.94=68.16rad/sec`

Now from second equation of motion we know that

`\Theta =\omega _it+(1)/(2)\alpha t^2=68.16* 3.3+(1)/(2)* 1.8* 3.3^2=224.928+9.801=234.729radian`