Question

# A wheel is at rest. Its angular velocity increases uniformly and becomes $80$ radians second after $5$ seconds. the total angular displacement is:

Open in App
Solution

## Step 1: Concept usedThe angular velocity $\left(\mathrm{\omega }\right)$ is assumed to rise evenly. The angular acceleration $\left(\mathrm{\alpha }\right)$ must always be the same.Given that it begins at rest and that the total angular velocity is$80$ rad/sec in $5$ seconds,${\mathrm{\omega }}_{\mathrm{i}}=0$${\mathrm{\omega }}_{\mathrm{f}}=80\mathrm{rad}/\mathrm{sec}$$\mathrm{t}=5\mathrm{sec}$Step 2: Calculation of circular motionBy the equation of circular motion, ${\mathrm{\omega }}_{\mathrm{f}}={\mathrm{\omega }}_{\mathrm{i}}+\mathrm{\alpha t}$$\mathrm{\alpha }=\frac{80}{5}$$=16\mathrm{rad}/{\mathrm{sec}}^{2}$Step 3: Find the total angular displacementThe expression to find the angular displacement is given as : $\mathrm{\theta }=12{\mathrm{\alpha t}}^{2}$ $=12×16×25$ $=200\mathrm{rad}\mathrm{as}\left({\mathrm{\omega }}_{\mathrm{o}}=0\right)$Therefore, the total angular displacement is $200\mathrm{rad}$.

Suggest Corrections
0