CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A rigid body rotates about a fixed axis with variable angular velocity equal to $$\alpha - \beta t$$, at time $$t$$ where $$\alpha,\ \beta$$ are constants. The angle through which it rotates before it stops:


Solution

Given $$\omega = \alpha -\beta t$$  
$$\Rightarrow w=\alpha - \beta t=0$$  $$\Rightarrow t=\dfrac{\alpha}{\beta}$$
$$\omega= \dfrac{d\theta}{dt}$$  $$\Rightarrow \dfrac{d\theta}{dt}=\alpha -\beta t$$
$$\Rightarrow d\theta= (\alpha -\beta t)dt$$   ...1
Integrate the equation 1  $$\Rightarrow \int{d\theta}= \int_{0}^{\frac{\alpha}{\beta}} {(\alpha -\beta t)} dt$$
$$\Rightarrow \theta= \dfrac{\alpha^2}{\beta}$$
Hence, Angle $$=\dfrac{\alpha^2}{\beta}$$ $$rad$$

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image