Mechanics 1

Question 1

Average Velocity

Answer 1

Vav = ∆x/∆t = 1/∆t ∫Vx dt

Question 2

Instantaneous Velocity

Answer 2

Vx (t) = dx/dt

Question 3

Average Speed

Answer 3

total distance / total time = s/t

Question 4

Average Acceleration

Answer 4

a av = ∆vx/ ∆t

Question 5

Instantaneous Acceleration

Answer 5

a = dv/dt = d²x/dt²

Question 6

Kinematic Equations for Constant Acceleration

Velocity

Answer 6

Vx = Vx0 + ax t

Question 7

Kinematic Equations for Constant Acceleration

Average Velocity

Answer 7

V avx = 1/2 (vx0 + vx)

Question 8

Kinematic Equations for Constant Acceleration

Displacement in Terms of V avx

Answer 8

= tV avx

Question 9

Kinematic Equations for Constant Acceleration

Displacement as a Function of Time

Answer 9

= Vx0 t + 1/2 ax t²

Question 10

Kinematic Equations for Constant Acceleration

Answer 10

Vx² = Vx0² + 2 ax ∆x

Question 11

Instantaneous-Velocity Vector

Answer 11

v = dr/ft

Question 12

Centripetal Acceleration

Answer 12

a = v²/r

Question 13

Circular Motion Time Period

Answer 13

v = 2πr / T

Question 14

Newton’s First Law

Answer 14

An object at rest stays at rest unless acted on by an external force. An object in motion continues to travel with constant velocity unless acted on by an external force.
Reference frames in which these statements hold are inertial reference frames

Question 15

Newton’s Second Law

Answer 15

The acceleration of an object is directly proportional to the net force acting on it.
F = ma

Question 16

Newton’s Third Law

Answer 16

When two bodies interact, the force Fba exerted by object B on object A is equal in magnitude and opposite in direction to the force Fab exerted by object A on object B.

Question 17

Inertial Reference Frames

Answer 17

Newton’s first and second laws are only valid in inertial reference frames

A reference frame that is moving with constant velocity relative to an inertial reference frame is itself an inertial frame

Any reference frame Acceleration relative to an inertial reference frame is not an inertial reference frame

Question 18

Hooke’s Law

Answer 18

Fx = -kx

Question 19

Work-Kinetic Energy Theorem

Answer 19

Wtot = ∆KE

Question 20

Scalar / Dot Product

Answer 20

A . B = ABcosϕ

Question 21

Mechanical Energy of a System

Answer 21

E mech = Ksys + Usys

Question 22

Work-Energy Theorem for Systems

Answer 22

Wext = ∆Emech - Wnc

Wext = work done on system by external forces
Wnc = work done by none conservative internal forces

Question 23

Conservation of Mechanical Energy

Answer 23

If no external forces do work on a system then:

Kf + Uf = Ki + Ui

Question 24

Total Energy of a System

Answer 24

Etot = Emech + Etherm + Echem + Eother

Question 25

Mass and Energy

Answer 25

E = mc²

Question 26

Photon Energy

Answer 26

E = hf

Question 27

Kinetic Energy in Terms of Momentum

Answer 27

K = ρ²/2m

Question 28

Coefficient of Restitution

Answer 28

e = speed of separation / speed of approach

Question 29

Angular Velocity

Answer 29

ω = dθ/dt

Question 30

Angular Acceleration

Answer 30

α = dω/dt

Question 31

Tangential Velocity

Answer 31

Vt = rω

Question 32

Tangential Acceleration

Answer 32

at = rα

Question 33

Kinetic Energy for Rotation About a Fixed Axis

Answer 33

K = 1/2 I ω²

Question 34

Kinetic Energy for a Rotating Object

Answer 34

K = 1/2 M Vcm² + 1/2 Icm ω²

Question 35

Torque

Answer 35

τ = r x F

Question 36

Vector Product

Answer 36

A x B = ABsinϕ

Question 37

Angular Momentum for a Point Particle

Answer 37

L = r x ρ

Question 38

Angular Momentum for a System Rotating About a Symmetry Axis

Answer 38

L = Iω

Question 39

Quantisation of Angular Momentum

Answer 39

L = √(l(l+1)) ħ