# Rotational dynamics with constant CM velocity

1. Dec 14, 2013

### trulyfalse

Hey PF!

1. The problem statement, all variables and given/known data
I've attached the problem to this post along with my free body diagram.

2. Relevant equations
Moment of inertia of a cylinder: 1/2MR^2

3. The attempt at a solution
Since the cylinder is moving at a constant velocity and is not slipping, ƩF = 0. For the torques around the instantaneous axis of rotation, we can see that Ʃt = -(1.2 m)(Ft1) - (0.4m)(Ft2). However, I'm not sure how to proceed from here, and also have a few conceptual questions related to rolling without slipping. In which direction does the force due to static friction act in these problems? Does it act in such a way that it opposes the translational motion of the object in question or does it act to oppose rotational motion?

EDIT: Just realized that I forgot Fn and Fg on my free body diagram, but they're not terribly pertinent to this problem anyway.

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Last edited: Dec 14, 2013
2. Dec 14, 2013

### TSny

Hey trulyfalse!

My suggestion is to forget the forces and torques. This is just a kinematics problem.

3. Dec 15, 2013

### ehild

That question is crucial: What does rolling without slipping mean? How is the linear velocity of the centre related to the angular velocity of rolling ?

TSny is right, this is a pure kinematic problem.

ehild

4. Dec 15, 2013

### haruspex

As others have posted, you don't need to worry about forces here, just the geometry. (Hint: the instantaneous centre of rotation of a rolling wheel is the point of contact with the surface.)
But to answer your question about friction, it acts to oppose relative motion of the surfaces in contact. For a car accelerating forwards, the driving wheels, if there were no friction, would spin on the road, so the friction there acts forwards from the road onto the wheels (pushing the car along). The idling wheels, were there no friction, would slide along without turning, so the friction there acts backwards, causing those wheels to rotate faster.