Sliding
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Photo Credit: Iowa State Photo Credit: Iowa State Photo Credit: Iowa State
Knowing and understand the trajectory of a pool ball is beneficial for future strategic moves in a game. The sliding velocity of a cue ball is being counter acted by the frictional force of the table. This interaction causes the ball to slide in a right or left direction. The ball continues to slide then reaches a point where it continues to roll in a straight line. This is due to the velocity and angular velocity being parallel to each other.
Finally, the ball performs a parabolic sliding trajectory where U acts as the normal force and V acts as the tangential force. The ball moving from X0 to X1 reaches the maximum of the curvature. The tangential force is orthogonal to the normal force therefore, the curve bends away from the normal force.
Finally, the ball performs a parabolic sliding trajectory where U acts as the normal force and V acts as the tangential force. The ball moving from X0 to X1 reaches the maximum of the curvature. The tangential force is orthogonal to the normal force therefore, the curve bends away from the normal force.
Slipping/Rolling
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Photo Credit: Real World Physics Problems Photo Credit: Real World Physics Problems
It is important to understand the slipping between the ball and the table. A1, A2, and A3 will have separate outcomes of slipping due to their location on the ball. When the ball is hit with leftward force in region A1, the ball gives a backspin in the clockwise direction and a leftward velocity. When the ball is hit with a leftward force in point A2, the ball gives a forward spin in the counterclockwise direction and a leftward velocity. Due to the frictional force, for both A1 and A2, the velocity of ball decreases and accelerates toward the rightward direction. When the ball is hit with a leftward force in region A3, the ball gives a forward spin in the counterclockwise direction. The velocity of the ball increases and accelerates to the left due to the direction of the frictional force. The frictional force develops due to the kinetic friction which occurs in the opposite direction.