Rotational dynamics - direction of friction

In summary, the conversation discusses rotational dynamics and the movement of a sphere in different scenarios with friction present. It raises questions about how friction affects the acceleration and angular acceleration of the sphere, and how the direction of static friction is determined. The summary also includes explanations for each scenario and the general concept of friction being opposite to the acceleration of the surfaces in contact.
  • #1
jaumzaum
434
33
I'm studying rotational dynamics and I've got a couple questions I can't answer. I want to describe de movement of the bodies in the cases below, the coefficient of friction in all the cases is [itex]\mu[/itex] . I will say what I think it would happen, and I would appreciate if you guys judge it right or wrong, as well as answering my other questions.

a = translational acceleration (acceleration of the center of mass)
γ = angular acceleration

http://img7.imageshack.us/img7/2407/88384154.png [Broken]

In (A) we have a sphere (I = 2/5 MR²) rotating without sliding in a horizontal plane. If we had friction to the right, a would increase and [itex]\gamma[/itex] would decrease, absurd because a = [itex]\gamma[/itex] R.
If we had a frictions to the left, a would decrease and [itex]\gamma[/itex] increase. Absurd too. So will the sphere stay rotating forever?

In (B) we have a sphere initially at rest at an inclined plane. If the sphere does not rotate, where is the friction? I would say the friction is upwards, as the sphere needs to increase both a and γ . Is it right?

In (C) we have a sphere initially moving up an inclined plane, without sliding. Is it possible? I mean; if there was a friction upwards, a would be increasing and γ decreasing, but if there was a friction downwards, a would be decreasing and γ increasing, both things are imposible. So is there impossible to be a sphere rolling up an inclined plane without sliding?

And a general question: How is the direction of the static friction determined generally? I've learned friction is opposite to the displacement of the body in relation to the plane of the friction but if we have a body rolling without sliding, the contact point have instantaneous velocity = 0, so there is no instantaneous displacement from the ground, where should the friction be?
 
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  • #2
jaumzaum said:
I'm studying rotational dynamics and I've got a couple questions I can't answer. I want to describe de movement of the bodies in the cases below, the coefficient of friction in all the cases is [itex]\mu[/itex] . I will say what I think it would happen, and I would appreciate if you guys judge it right or wrong, as well as answering my other questions.

a = translational acceleration (acceleration of the center of mass)
γ = angular acceleration

http://img7.imageshack.us/img7/2407/88384154.png [Broken]

In (A) we have a sphere (I = 2/5 MR²) rotating without sliding in a horizontal plane. If we had friction to the right, a would increase and [itex]\gamma[/itex] would decrease, absurd because a = [itex]\gamma[/itex] R.
If we had a frictions to the left, a would decrease and [itex]\gamma[/itex] increase. Absurd too. So will the sphere stay rotating forever?

The static friction is zero when the resultant of the other external forces is zero, and the ball rolls with constant velocity. In real life, there are other forces (rolling resistance, air resistance) which will make it stop sooner or later.

jaumzaum;4295263 In (B) we have a sphere initially at rest at an inclined plane. If the sphere does not rotate said:
a[/B] and γ . Is it right?

Friction acts against relative motion of the surfaces in contact. When kept in rest, the static friction is zero. If you release the ball, gravity acts downward along the slope, accelerating the CM of the ball. The ball would slide but then the surfaces in contact would move with respect to each other. Static friction prevents it, so instantaneously, the point of contact stays in rest. The static friction is opposite to the force of gravity along the slope.But gravity exerts torque with respect to the point of contact, so the ball starts to roll downward.

jaumzaum said:
In (C) we have a sphere initially moving up an inclined plane, without sliding. Is it possible? I mean; if there was a friction upwards, a would be increasing and γ decreasing, but if there was a friction downwards, a would be decreasing and γ increasing, both things are imposible. So is there impossible to be a sphere rolling up an inclined plane without sliding?
Yes, the ball can roll upward the slope. Have you tried to roll up a real ball along a real slope? What happened?

Gravity would decelerate the CM of the ball. To keep it rolling, (so keeping the contact surfaces in rest with respect each other) the angular speed has to slow down, too. So the static friction provides a torque with respect to the CM which decelerates rotation. So it points upward.

jaumzaum said:
And a general question: How is the direction of the static friction determined generally? I've learned friction is opposite to the displacement of the body in relation to the plane of the friction but if we have a body rolling without sliding, the contact point have instantaneous velocity = 0, so there is no instantaneous displacement from the ground, where should the friction be?
The static friction prevents relative motion of the surfaces in contact. Assume there is no friction first and figure out in what direction would the surface of the body in contact with the ground accelerate. Friction is opposite to it.

ehild
 
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  • #3
Thanks!
One last question:

The static friction prevents relative motion of the surfaces in contact. Assume there is no friction first and figure out in what direction would the surface of the body in contact with the ground accelerate. Friction is opposite to it.

ehild

The static friction if opposite to the resultant acceleration (if we consider no friction) so? I think it makes more sense now. I thought it was opposite to velocity (if we consider no friction). I was confused because if it was opposite to velocity, the case C, the velocity is upwards, so the static friction should be downwards. But if we consider the acceleration rule, the acceleration is downwards, so the static friction can be upwards. Is it right?
 
  • #4
Well, the static friction is against the possible relative motion of the surfaces in contact, which would happen without the force of friction. So it is against relative acceleration. Think of the case when a block sits on the plateau of a truck. The truck is accelerating and the block stays in rest on the plateau. What is the direction of the static friction?
First, static friction acts both on the block and on the truck. The two forces are opposite to each other.

The static friction hinders relative motion. Without it, the block would slide backwards. So the static friction exerted on the block points into the direction of the acceleration of the truck. The static friction provides the force that accelerates the block together with the truck. At the same time, the static friction exerted on the truck opposes the acceleration of the truck.

ehild
 
  • #5


Firstly, it is important to note that the direction of friction is always opposite to the direction of motion or impending motion. In rotational dynamics, this can be a bit tricky to determine because the motion is not just linear, but also involves rotation.

In case (A), if there is a frictional force to the right, it would indeed cause the translational acceleration (a) to increase and the angular acceleration (γ) to decrease. This is because the frictional force would act in the opposite direction of the translational motion, causing a decrease in the net force acting on the sphere and thus a decrease in the translational acceleration. Similarly, the frictional force would act in the same direction as the rotation, causing a decrease in the net torque and thus a decrease in the angular acceleration.

In case (B), if the sphere is initially at rest on an inclined plane, there would be no motion at all. Therefore, there would be no frictional force. Friction only arises when there is motion or impending motion.

In case (C), it is indeed impossible for a sphere to roll up an inclined plane without sliding. This is because, as you correctly pointed out, the frictional force would cause a decrease in both the translational and angular accelerations, making it impossible to have a simultaneous increase in both. In reality, the sphere would either slide or roll down the inclined plane, depending on the coefficient of friction and the angle of inclination.

As for your general question, the direction of static friction is determined by the direction of the net force acting on the body. If the net force is in the direction of motion, the frictional force will act in the opposite direction, and vice versa. In the case of a body rolling without sliding, the frictional force would act in the direction opposite to the motion of the contact point with respect to the ground. This is because the motion of the contact point is the same as the motion of the body as a whole, and the frictional force always acts in the opposite direction to the motion of the body.
 

1. What is rotational dynamics?

Rotational dynamics is the study of the motion of objects that rotate around an axis and the forces that cause that motion. It is an important branch of physics that helps us understand how objects, such as wheels and gears, move and interact with each other.

2. How is friction involved in rotational dynamics?

Friction is a force that opposes motion and is present in all types of motion, including rotational motion. In rotational dynamics, friction can act in two directions: parallel to the surface of rotation and perpendicular to the surface of rotation. The direction of friction depends on the direction of rotation and the point of contact between the rotating object and its surface.

3. What determines the direction of friction in rotational dynamics?

The direction of friction in rotational dynamics is determined by the right-hand rule. This rule states that if you point your right thumb in the direction of the rotating object's motion, then your fingers will curl in the direction of the friction force. If the object is rotating clockwise, then the friction force will act in the opposite direction of the object's motion, and vice versa.

4. How does the direction of friction affect an object's rotation?

The direction of friction can have a significant impact on an object's rotation. If the friction force is acting in the same direction as the object's motion, it will slow down or stop the rotation. On the other hand, if the friction force is acting in the opposite direction of the object's motion, it can speed up the rotation or even cause the object to spin in the opposite direction.

5. How can the direction of friction be manipulated in rotational dynamics?

The direction of friction can be manipulated in rotational dynamics by changing the point of contact between the rotating object and its surface. This can be done by adjusting the object's shape, size, or weight, or by changing the surface it is rotating on. Additionally, the direction of friction can be altered by applying external forces, such as pushing or pulling on the object in a specific direction.

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