Looking for classes? Ksquare Career Institute, Bengaluru →
A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $\theta$. The frictional force -
A
Decreases the rotational and translational motion
B
Dissipates energy as heat
C
Decreases the rotational motion
D
Converts translational energy to rotational energy
Detailed Solution
When a body rolls without slipping, the point of contact is momentarily at rest, so the friction acting is static friction and does no net work. Hence it does not dissipate energy as heat.
For a body rolling down an incline, friction acts up the incline.
It opposes the translational motion, reducing the linear acceleration from $g\sin\theta$ to $\dfrac{g\sin\theta}{1 + I/MR^2}$.
At the same time its torque about the centre ($fR$) produces the angular acceleration, i.e. it increases the rotational motion.
So the friction takes away part of the energy that would have gone into translation and puts it into rotation; the total mechanical energy is conserved.
Hence the frictional force converts translational energy to rotational energy.
For a body rolling down an incline, friction acts up the incline.
It opposes the translational motion, reducing the linear acceleration from $g\sin\theta$ to $\dfrac{g\sin\theta}{1 + I/MR^2}$.
At the same time its torque about the centre ($fR$) produces the angular acceleration, i.e. it increases the rotational motion.
So the friction takes away part of the energy that would have gone into translation and puts it into rotation; the total mechanical energy is conserved.
Hence the frictional force converts translational energy to rotational energy.