How Long Does It Take a Rolling Spool to Hit the Floor?

[willworkforfood]

"A string is wound around a solid cylindrical spool of mass 9.4 kg and radius .11 m. Assume the acceleration of gravity to be 9.8 m/s^2. If the spool is released from rest and rolls along the string and the distance to the floor is 9.06 meters, then how long in seconds will it take the spool to hit the floor?"

I'm having trouble solving this. I tried setting torque equal to torque r*m*g=moment of inertia*(a/r). After I solved for acceleraton I threw it into the linear kinematics equation 9.06=.5*a*t^2 to solve for time ..but it didn't work out so well because I got the wrong answer. Am I thinking about this incorrectly? What other method can I use?

Thanks all for your help.

Diagram seen below:

http://portfolio.iu.edu/whoblitz/rotationalproblem.PNG

 

[Tide]

Have you considered using energy conservation? That would tell you speed versus height which you may be able to integrate and find height versus time.

 

[quicknote]

I understand your frustration with trying to solve this rotational motion problem. It seems like you have the right idea by setting torque equal to torque and using the linear kinematics equation, but there may be a few factors that you are missing.

Firstly, when solving for acceleration using torque, you need to take into account the moment of inertia of the spool, which is not given in this problem. The moment of inertia is a measure of an object's resistance to rotational motion and it depends on the mass, shape, and distribution of mass of the object. Without this information, it will be difficult to accurately solve for acceleration.

Secondly, when using the linear kinematics equation, you need to consider the fact that the spool is not only moving vertically, but also rotating as it falls. This means that the distance traveled by the spool is not just 9.06 meters, but also includes the distance traveled by the spool due to its rotational motion. This will affect the value you use for acceleration in the equation.

To accurately solve this problem, you will need to use the principles of rotational motion, including torque, moment of inertia, and rotational kinematics equations. If you are still having trouble, I suggest seeking help from a physics tutor or consulting a textbook or online resources for more guidance on rotational motion problems.