Rotation Of Rigid Bodies

Question 1

What’s a rigid body?

Answer 1

*A body that have decinite shape,
*Composed of many particles that are of fixed distances from each other
*Also, their size is fixed

Question 2

Are rigid bodies possible?

Answer 2

Real bodies are not rigid because the particles in them are always in constant circular motion

Question 3

What’s the difference between rotational motion and circular motion?

Answer 3

Rotational motion = Axis of motion passes through the body. (But for uniform rotational motion, it passes through the center of mass/gravity)
Circular motion = Axis of motion doesn’t touch the body at all

Question 4

What’s angular displacement?

Answer 4

It is the angle substended by a rotating body.

Question 5

Unit and formula of angular displacement

Answer 5

*Unit is in radians
*1 radians = 180 degrees
*Theta = s/r (arc length/ radius)

Question 6

What’s Angular velocity

Answer 6

*It is the rate of change of angular displacement with time
* Omega = theta/t
*Unit is in rad/s

Question 7

What’s angular acceleration?

Answer 7

*Rate of change of angular velocity
*Can be gotten by differentiating angar velocity
* Also gotten as the second derivative of angular disacement
*Unit is in rad/s²

Question 8

Linear equivalents of angular motion

Answer 8

Linear parameters = Angular parameters
s = θ
v = ω
a = α
m = ζ (moment of inertia)
F = τ (torque)
Time, t remains the same in both instances

Question 9

What’s the significance of equating parameters of linear and angular motion?

Answer 9

Because the equations in linear format are also true in angular format

Question 10

Rotational Inertia?

Answer 10

Is the tendency of a rotating body to keep on rating, or a stationary one to not rotate.

Question 11

What’s center of mass/gravity?

Answer 11

It is the point in a body that can represent the whole body in dynamics

Question 12

How’s the rotational inertia of a multiparticulate body calculated?

Answer 12

It is gotten as the summation of the mass of each particle multiplied by the square of their distance from the center of mass.
I = m1r1² + m2r2² +…+mnrn²
I = summation (MiRi²)

Question 13

How is Kinetic energy of a rotating body calculated?

Answer 13

*The kinetic energy is the energy due to the rotating of the rotating body.
*K.E = 1/2 ζω²

Question 14

rotational K.E for a body of many particles

Answer 14

K.E = ∑(1/2Mₙvₙ²)
K.E = 1/2(ζω²)