billiard ball of mass M and radius R is initially moving with speed v0 without rotating. The ball slows down thanks to kinetic friction between the billiard ball and the table top, but starts rotating at the same time. Eventually, the ball rolls without slipping. The coefficient of kinetic friction between the table top is μk. Find the angular acceleration of the ball and the acceleration of the center of mass before it starts rolling without slipping. Find the speed of the center of mass when the ball starts rolling without slipping.

billiard ball of mass M and radius R is initially moving with speed v0 without rotating. The ball slows down thanks to kinetic friction between the billiard ball and the table top, but starts rotating at the same time. Eventually, the ball rolls without slipping. The coefficient of kinetic friction between the table top is μk. Find the angular acceleration of the ball and the acceleration of the center of mass before it starts rolling without slipping. Find the speed of the center of mass when the ball starts rolling without slipping.

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Question

A billiard ball of mass M and radius R is initially moving with speed v₀ without rotating. The ball slows down thanks to kinetic friction between the billiard ball and the table top, but starts rotating at the same time. Eventually, the ball rolls without slipping. The coefficient of kinetic friction between the table top is μ_k. Find the angular acceleration of the ball and the acceleration of the center of mass before it starts rolling without slipping. Find the speed of the center of mass when the ball starts rolling without slipping.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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