1) What part of an object follows a smooth path when the object is made to spin through the air or across a flat smooth surface?
2) Describe the motion of the CG of a projectile, before and after it explodes in midair.
3) What is suggested by a star that wobbles off center?
Same answer to all three questions. It is the center of mass that newton's First and Second laws apply to.
In question One there is no external force or moment, so the linear and angular momentums remain constant. In question 2 the center of mass of the projectile continues along the same parabolic path that it did when it was all one body. The same applies to the star in question 3. The center of mass does not wobble, therefore the star is not alone but there must be at least one other body like a planet other other star that is interacting with the star and the center of mass of the star-planet system does not change its momentum.
1) The part of an object that follows a smooth path when the object is made to spin through the air or across a flat smooth surface is called the center of mass (also known as the center of gravity).
2) The motion of the center of gravity (CG) of a projectile before it explodes in midair is a parabolic path determined by the projectile's initial velocity and the force of gravity acting on it. The CG follows a curved trajectory, forming an arc.
After the explosion, the motion of the CG of the projectile changes. The trajectory of the individual fragments or debris will depend on various factors such as mass, velocity, and air resistance. The CG of the exploded projectile may experience a sudden change in its direction or come to a stop, depending on the force and direction of the explosion.
3) When a star wobbles off center, it suggests the presence of an unseen companion, most likely a planet or another stellar body. This wobbling motion is known as stellar wobble or radial velocity. It occurs due to the gravitational tug between the star and the companion object. By observing the star's subtle shifts in position, astronomers can infer the presence of nearby planets or other objects. This technique, called the radial velocity method or Doppler spectroscopy, has been instrumental in discovering numerous exoplanets.
1) When an object spins through the air or across a flat smooth surface, the part that follows a smooth path is called the center of mass or center of gravity. The center of mass is the average position of all the mass in an object. It is the point around which the object's weight is evenly distributed.
To determine the center of mass, you can follow these steps:
- For simple geometric shapes, such as a sphere or a cylinder, the center of mass can be located at the geometric center of the object.
- For irregular shapes, you can use the method of balancing. Place the object on a narrow pivot, like a pencil tip or a string, and observe where it balances without tilting. The point directly above this balancing point is the center of mass.
2) Before a projectile explodes in midair, its center of gravity follows the trajectory determined by its initial velocity and the forces acting on it, such as gravity and air resistance. The path of the center of gravity is a parabolic curve, which is characteristic of projectile motion.
After the explosion, the motion of the center of gravity will depend on the resulting fragments and the individual velocities imparted on them. The pieces of the projectile will be influenced by various forces, such as gravity, air resistance, and any interactions with other objects in the surroundings. The motion of the center of gravity after the explosion can be quite complex and may not follow a predictable pattern.
3) When a star wobbles off center, it suggests the presence of an orbiting planet or some other massive object exerting gravitational influence on the star. This phenomenon is called stellar wobble or radial velocity method, which is a technique used in detecting and studying extrasolar planets (planets outside our solar system).
To observe this wobble, astronomers measure small shifts in the star's light spectrum, caused by the Doppler effect. As a star moves slightly towards us due to the gravitational pull of an orbiting planet, its spectrum shifts towards shorter wavelengths (blue shift). Similarly, as the star moves away, the spectrum shifts towards longer wavelengths (red shift). By analyzing these shifts, astronomers can infer the presence, mass, and orbital characteristics of the planet causing the wobble.