Rolling Ball on Horiz. Plane: Friction, Torque & Angular Vel.

[sr_philosophy]

Consider a ball rolling on a horizontal plane where friction is present. The forces acting on the ball are mg, friction at the contact and the normal force. This friction acts opposite to the direction of velocity. That should provide a clockwise torque and hence increase the angular velocity of the ball. Explain.

 

[tiny-tim]

Hi sr_philosophy!

Hint: where is the centre of rotation? and does it matter?

 

[astrokreng]

I would like to first clarify that the statement "friction acts opposite to the direction of velocity" is not entirely accurate. Friction is a force that opposes the relative motion between two surfaces in contact, and its direction depends on the direction of the applied force and the nature of the surfaces in contact.

With that being said, let's consider the scenario of a ball rolling on a horizontal plane with friction present. As the ball rolls, it experiences a downward force due to gravity (mg), a normal force from the surface it is rolling on, and a frictional force at the contact point between the ball and the surface. The frictional force acts in the opposite direction to the motion of the ball, as it tries to prevent the ball from sliding or slipping on the surface.

Now, let's focus on the rotational motion of the ball. The frictional force at the contact point creates a torque (or a turning force) on the ball. This torque is in the clockwise direction, as the frictional force is acting opposite to the direction of the ball's motion. This torque causes an angular acceleration, which in turn increases the angular velocity of the ball.

To better understand this, let's consider the concept of angular momentum. The angular momentum of an object is the product of its moment of inertia (a measure of how difficult it is to change its rotational motion) and its angular velocity. In this case, as the frictional force increases the angular velocity of the ball, its angular momentum also increases.

In summary, the frictional force acting on the ball in the opposite direction to its motion creates a clockwise torque, which increases the angular velocity of the ball. This is because the frictional force increases the angular momentum of the ball, causing it to rotate faster.