12. Which of the following statements is correct for a particle moving in a horizontal circle with constant angular velocity?
A. The linear momentum is constant but the kinetic energy varies.
B. The kinetic energy is constant but the linear momentum varies.
C. Both kinetic energy and linear momentum are constant.
D. Both speed and linear velocity are constant.
E. Neither the linear momentum nor the kinetic energy is constant.
The correct statement for a particle moving in a horizontal circle with constant angular velocity is:
B. The kinetic energy is constant but the linear momentum varies.
To determine the correct statement for a particle moving in a horizontal circle with constant angular velocity, we need to consider the concepts of linear momentum and kinetic energy.
Linear momentum is a vector quantity defined as the product of an object's mass and its velocity. It is conserved in a system when no external forces act upon it. In the case of a particle moving in a horizontal circle with constant angular velocity, the direction of velocity constantly changes, implying that the object is experiencing acceleration. Therefore, there must be a net force acting towards the center of the circle to keep it moving in the circular path. As a result, linear momentum is not constant in this scenario.
Kinetic energy, on the other hand, is the energy possessed by an object due to its motion. It is given by the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. In the case of a particle moving in a horizontal circle with constant angular velocity, the speed of the particle remains constant since the angular velocity is constant. However, the direction of velocity changes, implying that kinetic energy varies. As the particle moves, it experiences an inward net force, causing a change in velocity and therefore altering its kinetic energy.
Based on these explanations, we can conclude that the correct statement for a particle moving in a horizontal circle with constant angular velocity is:
B. The kinetic energy is constant, but the linear momentum varies.