PHY 101 Mock Test 1

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.

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.

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.

An event is a fundamental concept defined by its spatial coordinates (x, y, z) and its time coordinate (t).

This is the definition of a perfectly elastic collision.

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.

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

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.

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

For kinetic and maximum static friction, the force depends on the normal force and the coefficient of friction, not on the apparent area of contact.

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

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

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.

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

The boat’s velocity relative to the shore is the vector sum of its velocity across the river and the river’s velocity downstream. With both constant, the resultant is constant, leading to straight-line motion at an angle.

v_AB = v_A – v_B = (60 N) – (80 N) = -20 N, which is 20 km/h in the opposite direction (South).

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.

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

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

The law of conservation of momentum states that the total momentum of an isolated system remains constant. Mechanical energy is only conserved if non-conservative forces do no work.