Stuck on a Torque Problem Help is appreciated

[cngest]

Stuck on a Torque Problem! Help is appreciated!

1. A mass of 45.5kg is attached to a light string (negligible) that is wrapped around a cylindrical spool of radius 10cm and moment of inertia 4.0kg*m^2. The spool is suspended from the ceiling, and the mass is then released from rest a distance 3.5m above the floor. How long does it take to reach the floor?
2. Sum of the torques = Inertia * angular acceleration
3. I calculated the mass of the spool to be 400kg by using I=mr^2. After that, I'm directionless! Thanks in advance for your help :)

 

[azizlwl]

Distance is given and you are required to find time.
You can use SUVAT equation to find the time.
Another value you need to find is the accceleration.
Downward acceleration of the mass is also related to rotational acceleration of the spool.

 

[cngest]

that helps a bit but I'm still confused on how to calculate angular acceleration since i don't know ω...

 

[azizlwl]

that helps a bit but I'm still confused on how to calculate angular acceleration since i don't know ω...

You have find α not ω.
Just assume downward acceleration equal to a.
Then draw a fbd of the mass.

Assume a force is pulling 2 bodies connected by a string. But here the second body is a spool.

 

[Nickie]

Hello there,

I understand that you are stuck on a torque problem and are seeking help. I will do my best to guide you through the problem.

Firstly, it is important to understand the concept of torque. Torque is the measure of the force that causes an object to rotate about an axis. In this problem, the torque is caused by the gravitational force acting on the mass as it falls.

Now, let's break down the problem step by step:

1. The first step is to determine the forces acting on the system. In this case, we have the gravitational force acting on the mass and the tension force in the string. Since the string is light, we can neglect its weight.

2. Next, we need to find the net torque acting on the system. This can be calculated by multiplying the gravitational force (mg) by the distance between the point of rotation (the center of the spool) and the point where the force is applied (the center of the mass).

3. Using the formula for torque (T=Fr), we can calculate the torque caused by the gravitational force. Remember to use the radius of the spool (0.1m) as the distance in this calculation.

4. Now, we need to calculate the moment of inertia of the system. This can be done by adding the moment of inertia of the spool (4.0kg*m^2) and the moment of inertia of the mass (mr^2).

5. Finally, we can use the formula given in step 2 (Sum of the torques = Inertia * angular acceleration) to find the angular acceleration of the system.

6. With the angular acceleration known, we can use the equation of motion for rotational motion (θ=θ0+ω0t+0.5αt^2) to find the time it takes for the mass to reach the floor.

I hope this explanation helps you in solving the problem. Remember to always break down the problem into smaller steps and use the appropriate formulas and concepts. If you are still having trouble, don't hesitate to seek further assistance. Best of luck!