PHY 101 Mock Test 1

This is a common point of confusion. The two forces are an interaction pair between two different bodies, so they do not cancel for a single body.

It does not exchange matter or energy with its surroundings.
Explanation: An isolated system has no interactions across its boundary, no transfer of mass, heat, or work.

These mathematical functions are defined as power series. Adding quantities with units like meters or seconds inside them is physically meaningless; the argument must be a pure number.

By definition, the normal force is the component of contact force perpendicular (normal) to the surface. Its magnitude depends on the situation.

Rotational KE = (1/2)Iω². KE is proportional to ω², so doubling ω increases KE by a factor of 2² = 4.

When vectors are opposite (180°), they subtract. The resultant magnitude is |A – B|, which is smaller than when they are at any other angle

Displacement has both magnitude (distance) and direction. Temperature, mass, and time are scalars with magnitude only.

This is the operational definition: a frame where an object with no net force acting on it moves with constant velocity (or remains at rest).

This is a key consequence of Einstein’s theory of special relativity. Simultaneity is not absolute but depends on the observer’s state of motion.

The first law introduces the property of matter known as inertia, which is the tendency of an object to resist changes in its state of motion.

Dimensionally: [ML⁻¹T⁻²] = [ML⁻³]ᵃ [LT⁻¹]ᵇ. Solving gives: For M: 1 = a; for L: -1 = -3a + b → b=2; for T: -2 = -b → b=2.

Mechanical energy (KE+PE) is constant if the work done by all non-conservative forces (like friction) is zero.

Mechanical energy is lost to heat and sound (non-conservative forces). However, when considering all forms of energy, the total energy of the universe (ball + Earth + surroundings) is conserved.

Just as mass resists linear acceleration (F=ma), the moment of inertia (I) resists angular acceleration (τ=Iα).

Newton’s second law for a system states that the net external force equals the total mass times the acceleration of the center of mass. Internal forces cancel in pairs.

A · B = |A||B|cosθ. For θ = 90°, cos90° = 0, so the dot product is zero.

Impulse, J = ∫ F dt (or F_avg Δt for constant force), is a measure of the change in momentum it produces.

The ball has the train’s initial horizontal velocity relative to the ground. Under gravity alone, it follows projectile motion (a parabola) as seen by the ground observer.

α = dω/dt, analogous to linear acceleration a = dv/dt.

Multiplying by a negative scalar (-2) scales the magnitude by 2 and reverses the direction by 180 degrees.