Question

1. A rigid object with moment of inertia 0.4 kg mº is spinning with angular speed of 0.2 rad/s around a fixed axis. A constant torque of 0.6 Nm is applied that increases the rotation speed of the object (no other force is present). (i) Calculate the angular acceleration of the object. (ii) Calculate the angular speed of the object at t = 4 s. (iii) Calculate the angle spanned by the object from 0 s to 4 s.

Answer 1

(i) Angular acceleration

Consider the rigid object

Net Torque = Moment of inertia * Angular acceleration

$\tau _{net}=I\alpha$

$0.6Nm=0.4kgm^{2}*\alpha$

$0.6=0.4*\alpha$

$\frac{0.6}{0.4}=\alpha$

(i) ANSWER: ${\color{Red} \alpha =1.5rad/s^{2}}$

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(ii) Angular speed

Use formula $v=u+at$

$\omega =\omega _{0}+\alpha t$

$\omega =0.2rad/s+1.5rad/s^{2}*4s$

$\omega =0.2+1.5*4$

(ii) ANSWER: ${\color{Red} \omega =6.2rad/s}$

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(iii) Angular displacement

Use formula $s=ut+\frac{1}{2}at^{2}$

$\theta =\omega _{0}t+\frac{1}{2}\alpha t^{2}$

$\theta =0.2rad/s*4s+0.5*1.5rad/s^{2}*(4s)^{2}$

$\theta =0.2*4+0.5*1.5*4^{2}$

(iii) ANSWER: ${\color{Red} \theta =12.8rad}$

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