| Problem statement Solution video |
DISCUSSION THREAD
Ask your questions here. Or, answer questions of others here. Either way, you can learn.
DISCUSSION and HINTS
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw a free body diagram (FBD) of the disk.
Step 2: Kinetics (Newton/Euler)
Based on your FBD above, write down the linear impulse momentum and angular impulse/momentum equations for the disk.
Step 3: Kinematics
What kinematics do you need here to solve?
Step 4: Solve
From your equations in Steps 2 and 3, solve for angular velocity of the disk at time 2 and the reactions at O.
Since there is no gravity arrow, is it safe to assume that gravity isn't present?
I talked to the head TA during office hours, and he said to assume there is gravity. Usually, if something is in the horizontal plane, they are very clear about that from what I have seen.
Gravity is present, but it does not affect the rotation of the disk. Thus, we do not need to take it into account to find the angular velocity of the disk. However, it is used in the second part of the problem to find the vertical reaction force.
Since gravity is the only external force acting on the disk in the vertical direction but there is no translational motion,
Fy = R-mg = 0
Solving this, you can find the vertical reaction force at point O.
I included gravity in order to get the y component of my reaction force at pt. O.
I feel like it wouldn't make sense to not include gravity; I also included gravity to find reaction force for the y component.
Since the disk is pinned, would the acceleration for Newton's second law just be 0?
Yes, you can assume that the acceleration of the disk at point O would be 0. However, angular acceleration wouldn't be zero, so it would need to be considered.
To find the reaction forces at O, do you have to use linear impulse momentum, or can you just use newtons 2nd law?
Newton is fine.
The moment of inertia in the AIM equation is equal to 1/2 * m * r^2 correct?
Yes.
Do we have to account for friction on the rope since the rope does not slip on the disk?
I believe when setting the system to be the disk and the rope, friction would be an internal force that doesn’t impact your answer
In these types of problems, we model the entire disk as a single rigid body. The friction between the rope and the disk does not need to be shown separately in the free body diagram because it's part of the external force F applied at the rim. Since the rope does not slip, this force fully captures the effect of the rope's contact without needing to account for internal friction forces. Only external forces are included in the FBD of the disk.
If it is pinned, does that mean it is unable to spin?
The pin allows for rotation. If it did not, then it would not make sense to be asking for the angular velocity of the disk.