Question

a cd has a initial velocity of 1 rad/s and is given an angular acceleration of $\alpha$=30 (rad/s²), where theta is is in rad. What is the magnitudes of the tangential and normal components of acceleration at point P that is on the edge of the CD after the CD completes one rotation. The radius is 0.4m

Answer 1

Initial angular velocity $\omega _{0}=1 rad/s$

Angular acceleration $\alpha =30 rad/s^{2}$

Angular displacement of CD after 1 complete rotation=360⁰$=2\pi =2\times 3.14=6.28rad$

Using third equation of rotational motion-

$\mathbf{\omega^{2}= \omega_{0}^{2}+2\alpha \theta }$

$\mathbf{\omega^{2}= 1^{2}+2\times 30\times 6.28 }$

$\mathbf{\omega^{2}= 377.8}$

$\mathbf{\omega= 19.43rad/s}$

tangential acceleration of CD is given as-

$\mathbf{a_{tangential}=r\alpha }$

$\Rightarrow \mathbf{a_{tangential}=0.4\times 30 }$

$\Rightarrow \mathbf{a_{tangential}=12m/s^{2} }$

Radial acceleration after one rotation is given by-

$\mathbf{a_{radial}=r\omega ^{2}}$

$\mathbf{a_{radial}=0.4\times 19.43 ^{2}}$

$\mathbf{a_{radial}=151m/s^{2}}$ (approx.)