Angular Accelerations of Rigid Bodies with Applied Forces

In summary: Thanks!It's a pretty simple problem I think, but I may have overthought it and become confused. Help!Welcome to PF! :)You're confused because you're thinking that the rotation of a body might decrease (or increase) its acceleration.That would make a lot more sense! :)
  • #1
KBL-8
3
0
Edit: Tried to post three times and forum kept adding the prompts. Removed Prompts.

Homework Statement


Three blocks are initially at rest on a level frictionless surface. At t=0s, a three identical forces are applied to a different point on each block.
Each block is a rectangle approximately 3x1 oriented with the long sides facing north/south. The center of mass on each block is at (1.5,.5) if the lower left corner of the block is (0,0)

The force on block 1 is applied at about (1,.5)
The force on block 2 is applied at the center of mass
The force on block 3 is applied at about (3,.5)

img233.imageshack.us/img233/959/dynamicsofrigidbodiescq9.png

a) Draw an arrow on the diagram indicating the direction of acceleration of each blocks center of mass. If the acceleration is zero, state so explicitly.
b) Rank the center of mass accelerations from largest to smallest and explain. Draw a point FBD for each block

Homework Equations


Conceptual problem.

The Attempt at a Solution


I think that all the accelerations will be equal. Accelerations are equal at the center of mass regardless of where the force is applied. However I'm confused because it seems like some of the force should go to rotating the object, and if that is true, the accelerations of each of these objects centers of mass will be different.
So either B1=B2=B3 or B2>B1>B3. The FBDs would be different depending on each. If B1=B2=B3, they would be quite simple, just one vector pointing North, but if B2>B1>B3, there would be (I think) the same but with different magnitudes.

It's a pretty simple problem I think, but I may have overthought it and become confused. Help!
Thanks.
 
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  • #2
I'm going with B3>B1>B2. I'm basing this on the idea that the force has the biggest advantage with B3 because the surface is shouldering half the weight. Regardless of direction, the magnitude would be greater. Maybe?? heh
 
Last edited:
  • #3
Welcome to PF!

KBL-8 said:
I think that all the accelerations will be equal. Accelerations are equal at the center of mass regardless of where the force is applied. However I'm confused because it seems like some of the force should go to rotating the object, and if that is true, the accelerations of each of these objects centers of mass will be different.

Hi KBL-8! Welcome to PF! :smile:

You're confused because you're thinking that the rotation of a body might decrease (or increase) its acceleration.

Hint: what is the total acceleration of a body relative to its centre of mass? :smile:
 
  • #4
Theres an explanation here:

phys150.wikispaces.com/torque+on+blocks
 
  • #5
KBL-8 said:
… center of mass accelerations …

Hi KBL-8! :smile:

Are you sure the book isn't asking for the angular accelerations?

That would make a lot more sense! :smile:
 

FAQ: Angular Accelerations of Rigid Bodies with Applied Forces

What is the definition of "Kinematics of Rigid Bodies"?

Kinematics of Rigid Bodies is a branch of physics that studies the movement of objects or bodies without considering the forces that cause the movement. It focuses on describing the position, velocity, and acceleration of a rigid body as it moves through space.

What is the difference between "kinematics" and "dynamics"?

Kinematics deals with the motion of objects without considering the forces that cause the motion. Dynamics, on the other hand, studies the forces that cause the motion of objects. In other words, kinematics is concerned with describing the motion, while dynamics is concerned with explaining the causes of the motion.

What is a rigid body?

A rigid body is an idealized physical body that does not deform under external forces. It is assumed to have a fixed shape and size, and all points on the body remain at a fixed distance from each other at all times. Real-life objects may not behave as rigid bodies, but they can be treated as such in certain situations.

How is the motion of a rigid body described?

The motion of a rigid body is described using kinematic quantities such as displacement, velocity, and acceleration. These quantities are vectors, which means they have both magnitude and direction. They can be represented graphically using position-time, velocity-time, and acceleration-time graphs.

What are the three types of motion for a rigid body?

The three types of motion for a rigid body are translation, rotation, and general motion. Translation occurs when the body moves in a straight line, rotation occurs when the body spins around an axis, and general motion is a combination of both translation and rotation. These types of motion can be described using kinematic equations and concepts such as center of mass and moment of inertia.

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