Slipping Rolling Motion on Inclined Plane

[michelp]

TL;DR: I may have some problems with sign of convention and stuff

Attempt at solution and correct answer is attached. the linear acceleration indicates that the friction actually is in the same direction as linear speed.

Why is the angular acceleration anticlockwise here, against the direction of angular speed? Shouldn't angular speed increase? Please help

 

[Lnewqban]

Please, note that the value of the final angular velocity is 20t=24 rad/s.
The dynamic friction of the rotating-sliding cylinder with the rough inclined plane consumed part of the original rotational energy.

 

[michelp]

Please, note that the value of the final angular velocity is 20t=24 rad/s.
The dynamic friction of the rotating-sliding cylinder with the rough inclined plane consumed part of the original rotational energy.

I'm sorry, could you expand more on that?

 

[PeroK]

Why is the angular acceleration anticlockwise here, against the direction of angular speed? Shouldn't angular speed increase? Please help

The cylinder is initially spinning in a clockwise direction. The frictional force on the cylinder is down the incline. This provides a linear acceleration and a rotational deceleration.

 

[michelp]

The cylinder is initially spinning in a clockwise direction. The frictional force on the cylinder is down the incline. This provides a linear acceleration and a rotational deceleration.

so if I'm getting it right, it depends on the initial condition, right? if the cylinder at first only does translation, then the friction would be against the speed of center of mass, right?

 

[PeroK]

so if I'm getting it right, it depends on the initial condition, right? if the cylinder at first only does translation, then the friction would be against the speed of center of mass, right?

Yes. In that case, there will be linear deceleration and rotational acceleration until the state of rolling without slipping is reached.

 

[A.T.]

if the cylinder at first only does translation, then the friction would be against the speed of center of mass, right?

Yes, the direction of friction is opposite to the relative motion at the contact point. And that direction depends on: linear velocity of the center, angular velocity and radius.