Question

Find the angle between the vectors of the angular velocity and the angular acceleration at $t=10.0s$

• A. ${15}^{\circ }$
• B. ${14}^{\circ }$
• C. ${17}^{\circ }$
• D. ${13}^{\circ }$

Answer 1

The correct option is C ${17}^{\circ }$

angular acceleration $\overrightarrow{\alpha }=\dot{\overrightarrow{\omega }}\overrightarrow{\alpha }=a\hat{i}+2bt\hat{j}cos\theta =\frac{\overrightarrow{\alpha }\cdot \overrightarrow{\omega }}{\left|\overrightarrow{\alpha }\right|\left|\overrightarrow{\omega }\right|}cos\theta =\frac{a^{2}t+2b^2{t}^3}{\sqrt{a^2+4b^2{t}^2}\sqrt{a^2{t}^2+b^2{t}^4}}cos{\theta }_{(t=10)}=0.955\theta =17$