Question

The angle x through which a bicycle wheel turns is given by x = a + bt² + ct³ where a, b, and c are constants.

Calculate the velocity and acceleration of the wheel as a function of time.

Answer 1

$x = a+bt^2+ct^3$

$\text{The angular velocity of rotation is a vector numerically equal to the first derivative}$

$\text{of the angle of rotation of the body}$

$\vec\omega= x'=2bt+3ct^2$

$\text{Angular acceleration is a vector quantity equal to the first derivative}$

$\text{{of the angular velocity with respect to time}}$

$\vec\alpha=\vec\omega'=2b+6ct$

$\text{Answer : }\vec\omega= 2bt+3ct^2;\vec\alpha=2b+6ct$