PHY 101 Mock Test 1

A fundamental principle is that all terms in a valid physical equation must have the same dimensions. Dimensional analysis verifies this consistency but cannot determine dimensionless constants.

This principle asserts that the fundamental laws of motion are invariant (take the same form) for all observers moving with constant velocity relative to each other.

By definition, P_total = Σ (m_i * v_i) for all particles i.

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.

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.

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

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

A world line on a space-time plot shows an object’s position (space) at every moment (time).

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.

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.

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.

θ = ω₀ t + (1/2)αt²
Explanation: This is the rotational kinematic equation, analogous to s = u t + (1/2) a t² in linear motion.

W_net = ΔKE. This is a fundamental theorem derived from Newton’s second law, linking forces (via work) to changes in motion (via kinetic energy).

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.

The center of mass of any system under the influence of a uniform gravitational field follows the simple parabolic trajectory of a point mass.

With negligible external torque, L = Iω is constant. Decreasing I forces ω to increase to keep the product constant.

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.

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

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

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