Here f = μ kN.Ĭan you see the difference in rotational motion of the sphere between the no-slip and slipping cases? Here f ≠ μ kN.įor Part (b), the coefficient of friction is reduced such that slipping does occur. Solve your equations from Steps 3 and 4 for the angular acceleration of the drum and the acceleration of block B.įor Part (a), the coefficient of static friction between the sphere and the ramp is sufficiently large that the sphere does not slip as it rolls. Similarly, if you chose the upward direction of B to be positive in the Newton equation for B, then that is the positive sign convention for the acceleration of block B. That is, if you chose the CCW direction to be positive for moments back in Step 2, this becomes the positive sign conventions for the angular acceleration. Be careful in abiding by your sign conventions in this step. Use the fact that C is the center of rotation in relating the kinematics of the drum to the kinematics of block B. Please note that if you do use C, you will need to use the parallel axis theorem in finding the mass moment of inertia of the drum about C. Because of this, you are able to use C for your Euler (moment) equation. Note that since the drum does not slip on either cable, point C on the drum is the instant center for the drum, with the acceleration of C, therefore, pointing toward the center of mass O. Write down the Newton/Euler equations for the drum. Solve your equations above for the speed of block A.Īny questions? Please ask and answer questions in the threaded discussion below.ĭraw individual free-body diagrams for the drum and block. What is the speed of point B on the disk as compared to the disk's center E? (Refer back to C being the IC for the disk.) See the freeze-frame image below, and compare the speed of B with that of A. (Carefully study either the animation above - you can actually see the IC from this!) Locating this IC is critical for you in setting up and using the kinematics for this problem. Note that the instant center (IC) for the disk is the no-slip contact point C. Also, based on your FBD above, which, if any, force does nonconservative work on the system in your FBD? Determine the work done by such a force.You might consider using the no-slip, rolling contact point C as your reference point for the disk. For each KE expression, recall that your reference point for the rotational component needs to be either the center of mass of the body, or a fixed point on the rigid body.
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