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

Answer:

 Angular displacement will be 234.729 radian

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 $\omega _f=\omega _i+\alpha t$

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

Now from second equation of motion we know that

$\Theta =\omega _it+\frac{1}{2}\alpha t^2=68.16\times 3.3+\frac{1}{2}\times 1.8\times 3.3^2=224.928+9.801=234.729radian$