Yes, an object possessing momentum always has energy. Momentum and energy are interconnected properties of an object and are related through the laws of physics.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, momentum is expressed as p = m * v. Momentum is a vector quantity, meaning it has both magnitude and direction.
Energy, on the other hand, is a scalar quantity that comes in various forms such as kinetic energy, potential energy, thermal energy, etc. Kinetic energy (KE) is the energy associated with the motion of an object and is directly related to its momentum. The kinetic energy of an object is given by the equation KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
Since momentum depends on both mass and velocity, and kinetic energy depends on mass and the square of velocity, any object that possesses momentum will also possess kinetic energy. The magnitude of the object's momentum is directly proportional to its kinetic energy.
It's important to note that an object can have momentum and energy even when it's not in motion. For example, an object at rest still possesses energy due to its mass (rest energy) according to Einstein's famous equation E = mc^2, where E represents energy, m represents mass, and c represents the speed of light.
In summary, the presence of momentum implies the presence of energy, and the amount of energy depends on both the mass and velocity of the object.