Question 641
CBSE Class 11 Physics · Systems of Particles and Rotational Motion · Rotational dynamics
A 30 N pull unwinds a light rope from a hollow \(3\,\mathrm{kg}\) cylinder of radius \(0.40\,\mathrm{m}\) without slipping. Find angular acceleration and rope acceleration.
Solution to Question 641
Complete workingThe pull supplies torque FR. For a hollow cylinder, I=MR².
\[\begin{aligned}\tau &= FR\\&= I\alpha\\&= MR^2\alpha\end{aligned}\]
\[\begin{aligned}\alpha &= \frac{F}{MR}\\&= \frac{30}{(3)(0.40)}\\&= 25.0\ \mathrm{rad\,s^{-2}}\end{aligned}\]
\[\begin{aligned}a &= \alpha R\\&= (25.0)(0.40)\\&= 10.0\ \mathrm{m\,s^{-2}}\end{aligned}\]
Final answer
\[\alpha=25.0\ \mathrm{rad\,s^{-2}},\quad a=10.0\ \mathrm{m\,s^{-2}}\]