🔋College Physics I – Introduction Unit 4 Review

Most real-world problems involve more than one force acting on an object at the same time. The strategy for solving these problems is always the same: identify every force, break them into components, find the net force, then apply $F = ma$ .

Step 1: Identify all forces acting on the object.

Draw a free-body diagram and label each force:

Normal force acts perpendicular to the contact surface, pushing the object away from that surface
Tension pulls along the length of a string, rope, or cable. In a suspension bridge, for example, tension in the cables supports the roadway's weight
Friction opposes the relative motion (or attempted motion) between two surfaces. A sliding block on a table experiences kinetic friction opposing its slide
Applied forces are any external pushes or pulls you exert on the object, like pushing a cart forward

Step 2: Resolve forces into components.

Choose your coordinate axes (usually horizontal $x$ and vertical $y$ ). Break any angled forces into their $x$ and $y$ components using sine and cosine. Then add all the $x$ -components together and all the $y$ -components together to get the net force in each direction.

Step 3: Apply Newton's second law.

$\vec{F}_{net} = m\vec{a}$

This gives you one equation per direction. Use algebra (and trigonometry, if forces are at angles) to solve for whatever quantity is unknown.

Motion in Accelerating Reference Frames

An inertial reference frame is one that isn't accelerating. Newton's laws work perfectly in inertial frames without any modifications. The ground (approximately) is an inertial frame.

A non-inertial reference frame is one that is accelerating. Inside such a frame, objects seem to experience forces that have no real physical source. These are called fictitious forces (or pseudo-forces). You feel one every time an elevator starts or stops.

Apparent weight is the normal force you actually feel, which can differ from your true weight $mg$ when you're in an accelerating frame.

For a person standing on a scale inside an elevator, apply Newton's second law to the person. Taking upward as positive:

$N - mg = ma$

where $N$ is the scale reading (apparent weight) and $a$ is the elevator's acceleration. Rearranging:

$N = m(g + a)$

Elevator accelerating upward ( $a > 0$ ): the scale reads more than $mg$ . You feel heavier.
Elevator accelerating downward ( $a < 0$ ): the scale reads less than $mg$ . You feel lighter.
Freefall ( $a = -g$ ): the scale reads zero. This is the sensation of weightlessness.

When solving problems in accelerating frames, always identify the acceleration of the frame itself and account for it when writing your force equations.

Circular Motion and Centripetal Force

Any object moving along a circular path is constantly changing direction, which means it's accelerating even if its speed stays constant. That acceleration points toward the center of the circle and requires a net inward force called centripetal force.

$F_c = \frac{mv^2}{r}$

where $m$ is the object's mass, $v$ is its speed, and $r$ is the radius of the circular path.

Centripetal force is not a new type of force. It's just the label for whatever real force (or combination of forces) points toward the center and keeps the object curving. For a ball on a string swung in a circle, tension provides the centripetal force. For a car rounding a flat curve, static friction does the job. For a satellite in orbit, gravity is the centripetal force.

Integrating Kinematics and Dynamics

Kinematics and Force in Dynamics Problems

Kinematics describes how an object moves (position, velocity, acceleration) without asking why. Dynamics asks why by connecting forces to that motion through Newton's second law. Most problems require both: you use force analysis to find acceleration, then plug that acceleration into kinematic equations to find velocities, positions, or times.

The three most common kinematic equations (for constant acceleration) are:

$v = v_0 + at$
$x = x_0 + v_0 t + \frac{1}{2}at^2$
$v^2 = v_0^2 + 2a(x - x_0)$

Solving multi-step problems:

List all given quantities and identify what you need to find
Draw a free-body diagram and apply $F_{net} = ma$ to find the acceleration
Choose the kinematic equation that connects your knowns to your unknown
Solve algebraically, then substitute numbers at the end
Check units and whether the answer makes physical sense

For example, if a block slides down a ramp with friction, you'd first use the force equations to find the net acceleration along the ramp, then use kinematics to find how fast it's going at the bottom.

Impulse, Momentum, Work, and Energy

These concepts build directly on Newton's laws and will be covered in much greater depth in later units. Here's a brief preview of how they connect.

Momentum is the product of mass and velocity:

$p = mv$

Impulse is a force applied over a time interval, and it equals the change in momentum:

$F \Delta t = m \Delta v$

This is actually Newton's second law rewritten. A large force over a short time and a small force over a long time can produce the same change in momentum.

Work is the energy transferred to an object when a force moves it through a distance:

$W = Fd\cos\theta$

where $\theta$ is the angle between the force and the direction of motion. (When force and motion point the same way, $\cos\theta = 1$ and $W = Fd$ .)

Kinetic energy is the energy of motion: $KE = \frac{1}{2}mv^2$

Gravitational potential energy is stored energy due to height: $PE = mgh$

These quantities give you powerful alternative tools for solving problems, especially when forces vary or when you care about the final state but not the details of the path in between.

🔋College Physics I – Introduction Unit 4 Review