### One-Dimensional Motion of a Particle

• Define mass and linear momentum and explain the concept of a Newtonian reference frame.

• Write and explain Newton second Law of motion, and explain the concept of conservation of momentum.

• Systematically use Newton second law to analyze the motion of a particle acted upon by forces that are constant, and explicit functions of time, position, and velocity. Identify the appropriate initial conditions in each case, and describe physical examples of each case. This should be done for both rectilinear and curvilinear motion.

• Describe the concept of angular momentum of a particle, write Newton second law in terms of angular momentum, and describe the principle of angular momentum.

The resultant of all the forces acting on a particle is proportional to the acceleration of the particle.

The motion of the center of mass of any system of particles is governed by Newton’s second law, which is written as $\Sigma F_{ext} = M a_{cm}$

• $\Sigma F_{ext}$ is the vector sum of all the external forces acting on the system. Internal forces exerted by one part of the system on another must not be included.

• M is the total mass of the system.

• $a_{cm}$ is the acceleration of the system’s center of mass.

### Solved Example:

#### 30-1-01

A rope supports an empty bucket of mass 3.0 kg. Determine the tension in the rope when the bucket is accelerated upward at 2.0 $m/s^2$. (Take g = 10 m/s$^2$)

Solution:
Draw the Free Body Diagram of the bucket. $T - mg = ma$ $T = mg + ma = m (g + a) = 3 (10 + 2) = 36\ N$