This document defines rigid body rotation about a fixed axis and discusses rotational kinematics. It explains that a rigid body has a fixed size and shape, and its particles maintain constant relative positions during rotation. Rotational kinematics equations are provided for angular velocity, acceleration, period, frequency, and how linear acceleration varies by distance from the axis of rotation. An example problem calculates linear acceleration on a flywheel rim and revolutions completed over time.

1. Rigid Body Rotation about a Fixed Axis
A rigid body about a fixed axis of rotation.
▪ Defined as an object that has fixed size and shape.
- Relative positions of its constituent particles remain constant.
▪ By “fixed axis” mean:
- Axis must be fixed relative to the body and fixed in direction
relative to an inertia frame.

2. Rigid Body Rotation about a Fixed Axis
1. Rotational Kinematics(Ⅰ)
Form the definition of a radian(arc length/radius) we know,
θ = s/r

3. Rigid Body Rotation about a Fixed Axis
2. Rotational Kinematics(Ⅱ)
The average angular velocity,
The instantaneous angular velocity,
The period T is the time for one revolution and the frequency f is
the number of revolutions per second (rev/s).

4. Rigid Body Rotation about a Fixed Axis
3. Rotational Kinematics(Ⅲ)
The average angular acceleration,
The instantaneous angular acceleration,
Translational kinematics,
Rotational kinematics,

5. Rigid Body Rotation about a Fixed Axis
4. Rotational Kinematics(Ⅳ)
▪ The angular velocity of a rotating body is
the same relative to any point on it.
<Rolling>
▪ The increase in speed with distance from
the point of contact is easily seen in the
spokes of a bicycle wheel:
The ends of the spokes need the road are
fairly distinct, whereas those at the top
are blurred.

6. Rigid Body Rotation about a Fixed Axis
▪ Example
A flywheel of radius 20 cm starts from rest, and has a constant angular
acceleration of 60 rad/s2.
Find: (a) the magnitude of net linear acceleration of a point on the rim
after 0.15 s;
(b) the number of revolutions completed in 0.25 s.
Solution: