Newton's Laws
This law is summarized as "an object in motion stays in motion unless acted upon by an external force."
Newton's First Law (Inertia)
The unit of work and energy in the SI system.
Joule
The product of an object's mass and its velocity.
What is Momentum (or Linear Momentum)?
The rotational equivalent of mass. It measures the resistance of an object to changes in its rotation.
What is Moment of Inertia (or Rotational Inertia)?
The net force required to accelerate a 5 kg box at 4 m/s².
20 Newtons
A student pushes a 20 kg box 5 meters with a 50 N force. The work done is...
250 Joules?
A 0.5 kg ball moving at 10 m/s hits a wall and rebounds at 6 m/s. The magnitude of the change in momentum of the ball.
What is 8 kg m/s?
A force applied at a distance from a pivot point. The rotational equivalent of force.
What is Torque?
A heavy truck and a small car collide head-on. During the collision, which vehicle experiences the greater force, and which experiences the greater acceleration?
The forces are equal (Newton's 3rd Law), but the small car experiences the greater acceleration (Newton's 2nd Law, a = F/m).
A 10 kg object is lifted vertically at a constant speed of 2 m/s. The power required to lift it (use g=10 m/s²).
What is 200 Watts?
A ping-pong ball and a golf ball are moving at the same velocity. Which one has more momentum, and which one would require more impulse to stop?
The golf ball (greater mass = greater momentum). It also requires the greater impulse (Impulse = Δp, so larger momentum change = larger impulse)
A solid hoop (I = MR²) and a solid disk (I = ½MR²) have the same mass and radius. You apply the same torque to each. Which one will have the greater angular acceleration, and why?
The solid disk (smaller moment of inertia). Since τ = Iα, for the same torque, a smaller I results in a larger α
A student claims that a book resting on a table has no forces acting on it because "it's not moving." Identify the flaw in this statement and name ALL the forces acting on the book.
The flaw is confusing "no net force" with "no forces." The book has a downward gravitational force (weight) and an upward normal force from the table, which are equal and opposite (balanced), resulting in a net force of zero.
Two students do the same amount of work to lift identical boxes to the top of a shelf. Student A takes 2 seconds, Student B takes 5 seconds. Compare the work done and the power exerted by each.
Work is identical (same force, same distance), but Student A exerts greater power (Power = Work/Time, so shorter time = more power)
Identical cars are tested in crash barriers. Car A hits a solid concrete wall and stops instantly. Car B hits a barrier of crumple zones and takes 0.5 seconds to stop. Both cars had the same initial speed. Compare the impulse and the average force experienced by the drivers in both cars.
The impulse is the SAME for both (same mass, same Δv). However, the average force is GREATER for Car A (hitting the wall) because Force = Impulse / Time, and the stopping time is much smaller
A figure skater spins with her arms outstretched. She pulls her arms in close to her body. Explain in terms of angular momentum and rotational kinetic energy what happens to her spin rate, and where the extra kinetic energy comes from.
Her angular velocity increases (conservation of angular momentum: I decreases, so ω increases). Her rotational kinetic energy (KE = ½Iω²) increases because she does positive internal work (muscle work) pulling her arms inward against the centripetal force
Two blocks (m1=3kg, m2=2kg) are in contact on a frictionless surface. A 15 N force is applied to m1. The magnitude of the force that m1 exerts on m2.
6 Newtons
A man pushes a 100 kg crate up a 30-degree frictionless incline. He pushes parallel to the incline for a distance of 4 meters. The work done by gravity during this push.
What is -1960 Joules?
A student argues: "If two objects have the same kinetic energy, they must have the same momentum." Is this true? Provide a mathematical counterexample to prove your point, and explain the physical difference between momentum and kinetic energy.
False. Example: A 1 kg object at 10 m/s has KE=50 J and p=10 kg·m/s. A 4 kg object at 5 m/s has KE=50 J but p=20 kg·m/s. Momentum is a vector (direction matters) and depends linearly on velocity, while KE is a scalar and depends on the square of velocity
A student solving a collision problem states: "Because there is no external torque, angular momentum is conserved. Therefore, the rotational kinetic energy must also be conserved." Is the student correct? Give a clear counterexample (like the skater or an inelastic rotational collision) to explain why energy is NOT always conserved even when angular momentum is.
Incorrect. Angular momentum is conserved, but kinetic energy is not conserved if the collision is inelastic (e.g., a spinning disk drops onto another stationary disk and they stick together via friction). Some mechanical energy is converted into thermal energy/sound/deformation. The skater is also a counterexample—her KE increases due to internal work, so it's not conserved either