Rotational Motion/Angular Momentum

[PhysicsNewb]

Hi, I'm stuck on two physics HW questions, and I'd like some help. Here are the questions and my (probably incorrect) work on them:

1) A disc of mass M, radius R, Icm = 1/2MR^2 is rolling down an incline dragging a mass M (block) attached with a light rod to a bearing at the center of the disc. The friction coefficients are the same for both masses, us, uk.

I need to determine the linear acceleration of the mass M and the friction force acting on the disc, as well as the tension in the rod.

I did sum of torques = I(rotational acceleration) and found the linear acceleration to be 2(fs)/M.

To find the frictional force acting on the disc I did two separate sum of forces equations and combined them to solve for fs, the only friction force acting on the disc alone.

Tension in the rod was found by putting numbers into one of the original sum of forces equations.

Are these steps correct? If not, could you please point me in the general direction of arriving at a correct response. Thank you.

2) A mass M is dropped from a Height H onto one end of a stick of mass M, length L, pivoted about ithe opposite end. Moment of inertia of the stick about the pivot is 1/3ML^2. Mass adheres to stick after collision.

I need to find the angular speed of the system after impact, linear speed of the mass M at its lowest point, and determine mechanical energy lost as a result of the collision.

To do this I first found the linear speed of the dropped mass to be sqrt2gH. Then I found the angular speed to be 2MLsqrt2gH/(M + M). Is this right?

I then found the linear speed at its lowest point to be L^2sqrt2gH/2 ny using the v cm = r(rotational velocity) equation.



About now I'm stuck with all those numbers above. I think they're wrong, but I don't know what to do next. Thanks in advance for any pointers.

 

[Doc Al]

Welcome to PF!

Regarding problem #1, there are several ways to get the answer. Your method looks fine to me.

For problem #2:

2) A mass M is dropped from a Height H onto one end of a stick of mass M, length L, pivoted about ithe opposite end. Moment of inertia of the stick about the pivot is 1/3ML^2. Mass adheres to stick after collision.

Are we to assume that the stick is just sitting there in a horizontal position at the time of impact?

I need to find the angular speed of the system after impact, linear speed of the mass M at its lowest point, and determine mechanical energy lost as a result of the collision.

To do this I first found the linear speed of the dropped mass to be sqrt2gH.

Looks good.

Then I found the angular speed to be 2MLsqrt2gH/(M + M). Is this right?

No. (The units don't even make sense.) To find the angular speed just after impact, use conservation of angular momentum. What's the angular momentum of the falling mass? What's the rotational inertia of the "stick + mass" system?

To find the mechanical energy lost during the collision, calculate the KE before and after the collision. Hint: After the collision, the system can be viewed as being in pure rotation about the pivot point.

To find the speed of the mass at the lowest point, use conservation of energy. Hint: Find the change in gravitational PE of the stick and mass in moving from a horizontal position to a vertical postion.

 

[wais]

Hi there,

First of all, let me commend you for showing your work and asking for help when you're stuck. It's always a good idea to check your work and make sure your steps are correct.

For the first question, your steps seem to be in the right direction. However, I would recommend using the equations for rotational motion and linear motion separately, rather than trying to combine them. For the rotational motion, you can use the equation T = Iα to find the rotational acceleration, and then use the equation a = αr to find the linear acceleration. For the linear motion, you can use the equations ∑F = ma and ∑F = μmg to find the friction force and then solve for the tension in the rod.

For the second question, your approach seems to be correct. However, I would advise you to be careful with your units when plugging in numbers. Make sure all the units are consistent and that you're using the correct equations for rotational motion. Also, for finding the angular speed after impact, you can use the equation L = Iω to find the angular momentum before and after the collision, and then use the conservation of angular momentum to solve for the final angular speed.

In terms of finding the mechanical energy lost, you can use the conservation of mechanical energy to solve for the initial and final kinetic energies, and then find the difference to determine the energy lost in the collision.

I hope this helps and points you in the right direction. Keep up the good work!