Newton's Laws
This law says an object at rest stays at rest, and an object in motion keeps moving at constant velocity, unless a net force acts on it.
Newton's First Law (the law of inertia)
Objects keep doing what they're already doing. Changing motion takes a net force.
This model shows every force on ONE object as an arrow drawn from a dot.
A free-body diagram (FBD)
Each arrow is a real force with an agent, pointing the way it pushes or pulls.
What is the weight of a 50 kg student?
490 N
F_g = mg = (50 kg)(9.8 m/s²) = 490 N
An object moves in a circle at constant speed. Which way does its acceleration point?
Toward the center of the circle
That's why it's called centripetal ("center seeking") acceleration.
The gravitational force between two objects depends on these two things.
Their masses and the distance between their centers
F_g = G m₁m₂ / r². More mass means more force. More distance means less force.
A 20 N net force acts on a 4 kg cart. What is the cart's acceleration?
5 m/s²
a = F_net / m = 20 N / 4 kg = 5 m/s²
A book sits still on a table. Name the two forces on its free-body diagram and their directions.
Weight (gravity) down, and normal force up
The book is at rest, so the two arrows are equal length and F_net = 0.
What are the units of the coefficient of friction, μ?
None. μ has no units.
μ = f / F_N is newtons divided by newtons, so the units cancel.
You whirl a stopper on a string, and the string snaps. What path does the stopper take?
A straight line, tangent to the circle
Inertia. With no inward force, nothing bends its path anymore. It does NOT fly straight outward.
You double the mass of ONE of the two objects. What happens to the gravitational force?
It doubles
Force is directly proportional to each mass.
A truck hits a bug on the highway. Which one feels the bigger force? Which one has the bigger acceleration?
Same size force on both. The bug has the much bigger acceleration.
Third Law: forces come in equal and opposite pairs. The bug's tiny mass gives it a huge a = F/m.
A skydiver falls at terminal velocity (constant speed). What is the net force on her, and how do her two arrows compare?
F_net = 0 N. Air resistance up is equal to weight down.
Constant velocity means a = 0, so the forces are balanced. She is still moving, but moving does not need a net force.
A 250 g mass hangs perfectly still from a spring scale. What does the scale read?
2.45 N
Convert first: 250 g = 0.250 kg. At rest, tension = weight = (0.250)(9.8) = 2.45 N.
Is centripetal force a new kind of force? Name the real force that keeps a car on a flat, curved exit ramp.
No. It's static friction from the road.
Centripetal force is a job, not a new force. Real forces (friction, tension, gravity) fill that job.
You double the distance between two objects. What happens to the gravitational force?
It drops to one quarter (1/4)
Inverse square: 1/(2²) = 1/4.
The same net force acts on Cart A (mass m) and Cart B (mass 3m). How does Cart B's acceleration compare to Cart A's?
One third as big
a = F/m. Triple the mass with the same force gives one third the acceleration.
A 6 kg box has a 30 N push to the right and 12 N of friction to the left. Find its acceleration.
3 m/s² to the right
F_net = 30 N − 12 N = 18 N right. a = 18 N / 6 kg = 3 m/s².
A 40 kg box slides across the floor. μ_k = 0.25. Find the kinetic friction force.
98 N
F_N = mg = (40)(9.8) = 392 N. f_k = μ_k F_N = (0.25)(392) = 98 N.
A 60 kg rider on a swing ride moves at 6 m/s in a circle with radius 8 m. Find the centripetal acceleration and centripetal force.
a_c = 4.5 m/s², F_c = 270 N
a_c = v²/r = 36/8 = 4.5 m/s². F_c = ma_c = (60)(4.5) = 270 N.
You TRIPLE the distance between two objects. What happens to the gravitational force?
It drops to one ninth (1/9)
Inverse square: 1/(3²) = 1/9.
A hockey puck slides EAST across the ice and is slowing down. Which way do the net force and the acceleration point?
Both point WEST
Slowing down means a points opposite the velocity. Net force always points the same way as a. Motion direction does not tell you force direction.
A student's free-body diagram of a sliding box includes an arrow labeled "ma." What's wrong with it?
ma is not a force. Take the arrow off.
Every arrow needs an agent (Earth, the floor, a rope). ma is the RESULT of adding up the real forces, not one more force.
You push a 25 kg toolbox with 120 N. μ_k = 0.35. Find its acceleration.
About 1.37 m/s²
F_N = 245 N. f_k = (0.35)(245) = 85.75 N. F_net = 120 − 85.75 = 34.25 N. a = 34.25 / 25 = 1.37 m/s².
A stopper whirls in a circle with radius 0.60 m. One trip around takes 0.50 s. Find its speed and its centripetal acceleration.
v ≈ 7.54 m/s, a_c ≈ 94.7 m/s²
v = 2πr/T = 2π(0.60)/0.50 = 7.54 m/s. a_c = v²/r = (7.54)²/0.60 = 94.7 m/s².
You double BOTH masses AND double the distance. What happens to the gravitational force?
It stays the same
Doubling both masses gives 2 × 2 = 4 times the force. Doubling distance gives 1/4. And 4 × 1/4 = 1.