Chapter 16

Question 1

When will just translation result from a force?

Answer 1

When the force is applied directly towards the centre of mass

Question 2

What is the equation for the translation of an object when a force has been applied?

Answer 2

F = ma

Question 3

What is the motion produced when a force is applied away from the centre of mass?

Answer 3

Translation and rotation will occur

Question 4

What is the equation for the moment produced from angular acceleration?

Answer 4

M = Jα

Question 5

What is the equation for momentum?

Answer 5

P = mv

Question 6

How is force calculated from momentum?

Answer 6

F = dp/dt

Question 7

What is the equation to calculate acceleration from momentum?

Answer 7

F = dp/dt
ma = dp/dt
a = (dp/dt)/m

Question 8

What is the equation for angular momentum?

Answer 8

L = Jω

Question 9

What is the equation to calculate the moment applied from angular momentum?

Answer 9

M = dL/dt

Question 10

What is the equation to calculate angular acceleration from angular momentum?

Answer 10

M = dL/dt
Jα = dL/dt
α = (dL/dt)/J

Question 11

How is the centre of mass calculated for non uniform shapes?

Answer 11

It is broken into uniform shapes and then the masses of those shapes are multiplied by their distances from a reference point and then the sum of all these shapes is divided by the total mass to get the point of centre of mass.

Question 12

What is the equation to calculate the centre of mass for a non-uniform shape?

Answer 12

x = Σm[i]x[i] / Σx[i]

Question 13

What is the equation for the tangential forces applied to an object?

Answer 13

ΣF[r] = m × a[g] = mω^2r
ΣF[t] = m × a[g] = mαr

Question 14

What is the equation for a calculating the mass moment of inertia from mass and radius of an object?

Answer 14

J = (mr^2)/2

Question 15

What is the symbol and unit of mass moment of inertia?

Answer 15

Symbol: J
Unit: kgm^2

Question 16

Is mass moment of inertia the same as the second moment of area?

Answer 16

Yes

Question 17

What is the equation to calculate the mass moment of inertia from the radius of gyration?

Answer 17

J = mk^2

Question 18

What is the equation to calculate the radius of gyration from the mass moment of inertia?

Answer 18

K = √(J / M)

Question 19

Where does mass moment of inertia apply?

Answer 19

Through the centre of mass usually but it can apply about any axis

Question 20

What is the equation for the mass moment of inertia about a parallel axis to the mass moment of inertia through the centre of mass?

Answer 20

I[0] = I[g] + mr^2
m = total mass
r = Distance between the parallel axis and the axis through the centre of mass