Rotational motion, frictionless.

[azizlwl]

http://img444.imageshack.us/img444/8148/rollwx.jpg

A rope is wound around a cylinder of mass 4kg, and I=0.02kg.m² about the cylinder axis.
The frictional force between table and cylinder is negligible.

Solution:
a=20/4=5.0m/s²
α=ar is not applicable when slippage occurs.


My question.
1.Is the cylinder moves forward with acceleration a without any rotation.
2. Is Fr=Iα is still applicable in this case, even though we know α=ar not applicable.
3. If we play yo-yo in zero gravity environment,how does the yo-yo behave when we pull it?

Thank you.

 

[K^2]

1. No, see 2.
2. Yes, Fr=Iα is always applicable. α=ar constraint is only needed for rolling, and is achieved via additional force, that being the force of friction. When no friction is present, you just compute angular and linear accelerations separately.
3. Yo-yo in zero-g will behave exactly the same as this test case. It will accelerate and spin in direction it's being pulled.

 

[azizlwl]

Thank you.
That really helpful since the book didn't say about rotation only a=αr is not applicable.

 

[haruspex]

A nice question to ask here is to find the instantaneous centre of rotation.

 

[PJC01]

1. Yes, the cylinder will move forward with an acceleration of 5.0m/s2 without any rotation due to the absence of friction on the table. This means that the torque generated by the tension in the rope is greater than the torque caused by the moment of inertia of the cylinder, resulting in no rotation and only linear motion.
2. Yes, Fr=Iα is still applicable in this case. This equation represents the relationship between the applied force (tension in the rope) and the resulting angular acceleration of the cylinder. Even though α=ar is not applicable in this scenario, the equation still holds true as long as there is no slippage between the cylinder and the table.
3. In a zero gravity environment, the yo-yo will behave differently depending on the initial conditions. If the yo-yo is initially at rest, pulling it will cause it to accelerate downwards due to the tension in the string. As the yo-yo moves downwards, the string will start to unwind and the yo-yo will start to rotate. If the yo-yo is initially spinning, pulling it will cause it to accelerate in the opposite direction of its rotation, slowing down its spin. However, without the force of gravity, the yo-yo will not be able to unwind the string and will continue to spin at a constant rate.