What is the magnitude of the acceleration of cylinder's com?

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Homework Help Overview

The discussion revolves around determining the magnitude of the acceleration of the center of mass of a uniform solid cylinder subjected to a constant horizontal force. The problem involves concepts from dynamics, specifically relating to torque and the motion of rigid bodies.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the use of torque to analyze the forces acting on the cylinder, with one participant expressing confusion about the application of torque and attempting to set up the equations. Others suggest using the parallel axis theorem and applying Newton's equations to eliminate frictional forces.

Discussion Status

The discussion is active, with participants questioning the setup of the torque equation and clarifying concepts such as the parallel axis theorem. There is a focus on understanding the forces at play and how they contribute to the net torque acting on the cylinder.

Contextual Notes

Participants are navigating the complexities of the problem, including the roles of different forces and torques, and there is an emphasis on ensuring clarity in the equations being used. The original poster expresses confusion about the approach, indicating a need for further exploration of the concepts involved.

JessicaHelena
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Homework Statement


In the figure below, a constant horizontal force
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app of magnitude 18 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 19 kg, its radius is 0.11 m, and the cylinder rolls smoothly on the horizontal surface.
(a) What is the magnitude of the acceleration of the center of mass of the cylinder?

Homework Equations

The Attempt at a Solution



I'm confused... I feel like I could use torque — I could set the bottom point as the origin, and then tau_net = 18 x 2 x 0.11 + F_cm x 0.11.
However, I couldn't really get further than that and I am really confused. Could someone help me?
 

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Taking torque about the bottom point is a convenient way of eliminating
the frictional force.
Are you familiar with the parallel axis theorem?
You can also apply Newton's equations about the center of mass
to eliminate the frictional force.
 
@J Hann — what's the parallel axis theorem?
 
JessicaHelena said:
@J Hann — what's the parallel axis theorem?
The moment of inertia I of a body about any axis is equal to the moment of inertia
I CM of the body about a parallel axis through its center of mass plus the mass M of the
body times the square of the perpendicular distance L between the axes:
I = Icm + M L^2.
For a cylinder about an edge I = 1/2 M R^2 + M R^2 = 3/2 M R^2
 
JessicaHelena said:
tau_net = 18 x 2 x 0.11 + F_cm x 0.11.

Taking the torque around the contact point was a very good idea. (Why?) However, your equation for the net torque is wrong. How many forces are there acting on the cylinder? And how many of those produce a torque about the contact point?
 

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