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visuality

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In summary, when a uniform ball is rolling without slipping on an inclined plane, gravity does not provide a torque, but it does provide a translational force. The force of gravity acts as if it were applied at the ball's center of mass, so there is zero offset between the point of application and the axis of rotation, resulting in zero torque. However, the force of gravity can be added to other forces acting on the ball to determine its net force and translational acceleration. Additionally, the torque from gravity can be added to other torques to determine the net torque on the ball, which can then be used to calculate the rate of change of angular momentum. Ultimately, the force of gravity does not contribute to the rotation of the ball around

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blue_leaf77

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jbriggs444

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Whether a force provides a torque depends on the axis of rotation you use. The force of gravity acts as if it were applied at an object's center of mass.visuality said:

If you use the ball's center of mass as the chosen axis of rotation then there is zero offset between the point of application and the axis of rotation. Zero moment arm means zero torque.

If you use the point where the ball touches the inclined plane (the momentary center of rotation) as the chosen axis then there is a perpendicular offset between the point of application and the chosen axis of rotation. Non-zero force multiplied by non-zero perpendicular offset means non-zero torque.

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visuality

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I'm new and not sure how to properly quote the above but jbriggs444 posted that.

Wow I never thought about a momentary center of rotation. I think I understand it now!

This isn't a homework question I'm just trying to understand something, If i wanted to find the force of gravity with F=ma would i have to add the translational acceleration and the angular acceleration? Or do I ignore the translational acceleration? Or something else?

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jbriggs444

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If you already know an object's mass then you can simply multiply by the acceleration of gravity (9.8 meters per secondvisuality said:This isn't a homework question I'm just trying to understand something, If i wanted to find the force of gravity with F=ma would i have to add the translational acceleration and the angular acceleration? Or do I ignore the translational acceleration? Or something else?

The force of gravity can be added to all the other forces acting on an object (do you know how to draw a "free body diagram"?) to determine the net force on the object and therefore its translational acceleration.

The torque from gravity can be added to all the other torques acting on an object to determine the net torque on the object (about the chosen reference axis). This will give you the rate of change of angular momentum. Angular momentum can be split into two parts:

1. The rotation of an object around its center of mass.

2. Movement of the center of mass relative to the chosen axis of rotation. Multiply the object's linear momentum by its mass and by the perpendicular offset from the chosen axis. [technically you are computing a vector cross product]

If you already know the translational acceleration of the object (having done your free body diagram and added up the forces) and you know its offset from the chosen axis then you can calculate the rate of change of part 2. If you know all of the torques then you know how total angular momentum is changing. The difference is the rate at which angular momentum is accumulating in or being drained from the object's rotation. Divide by the moment of inertia and you have angular acceleration.

It can be convenient to choose an axis of rotation that coincides with an object's center of mass. Then the second part of angular momentum is sure to be zero and all you have to worry about is the first part.

Torque and force are two different physical quantities that are related to each other in the context of ball rolling without slipping. Force is a vector quantity that describes the push or pull on an object, while torque is a vector quantity that describes the rotational effect of force on an object. In the case of a ball rolling without slipping, both torque and force are acting on the ball to cause it to roll.

Torque and force both contribute to the overall motion of a ball rolling without slipping. Force is responsible for the linear motion of the ball, while torque is responsible for the rotational motion. Together, they determine the speed and direction of the ball's movement.

In the context of ball rolling without slipping, the moment of inertia is a measure of the ball's resistance to rotational motion. The relationship between torque, force, and moment of inertia can be described by the equation τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. This equation shows that torque and moment of inertia are directly proportional, while torque and angular acceleration are inversely proportional.

Friction is an important factor in determining the torque and force of a ball rolling without slipping. Friction between the ball and the surface it is rolling on creates a torque that opposes the direction of motion, resulting in a decrease in the ball's speed. This frictional force also contributes to the overall force acting on the ball, affecting its linear motion.

There are many real-life examples of torque and force in ball rolling without slipping. One example is a bowling ball rolling down the lane without slipping. In this case, the force and torque from the bowler's hand cause the ball to roll forward with both linear and rotational motion. Another example is a rolling pin used in cooking, where the force and torque from the hands cause the pin to roll and flatten dough. In both examples, the concept of torque and force are essential in understanding the motion of the rolling objects.

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