1. Rotational Kinematics
Chapter 8
Rotational Kinematics

2. 8.1 Rotational Motion and Angular Displacement
In the simplest kind of rotation,
points on a rigid object move on
circular paths around an axis of
rotation.

3. 8.1 Rotational Motion and Angular Displacement
The angle through which the
object rotates is called the
angular displacement.

4. 8.1 Rotational Motion and Angular Displacement
DEFINITION OF ANGULAR DISPLACEMENT
When a rigid body rotates about a fixed axis, the angular
displacement is the angle swept out by a line passing through
any point on the body and intersecting the axis of
rotation perpendicularly.
By convention, the angular displacement
is positive if it is counterclockwise and
negative if it is clockwise.
SI Unit of Angular Displacement: radian (rad)

5. 8.1 Rotational Motion and Angular Displacement
For a full revolution:

6. 8.2 Angular Velocity and Angular Acceleration
DEFINITION OF AVERAGE ANGULAR VELOCITY
SI Unit of Angular Velocity: radian per second (rad/s)

7. 8.2 Angular Velocity and Angular Acceleration
Changing angular velocity means that an angular
acceleration is occurring.
DEFINITION OF AVERAGE ANGULAR ACCELERATION
SI Unit of Angular acceleration: radian per second squared (rad/s2)

8. 8.3 The Equations of Rotational Kinematics
Recall the equations of kinematics for constant acceleration.
Five kinematic variables:
1. displacement, x
2. acceleration (constant), a
3. final velocity (at time t), v
4. initial velocity, vo
5. elapsed time, t

9. 8.3 The Equations of Rotational Kinematics
The equations of rotational kinematics for constant
angular acceleration:
ANGULAR ACCELERATION
ANGULAR VELOCITY
TIME
ANGULAR DISPLACEMENT

10. 8.3 The Equations of Rotational Kinematics

11. 8.3 The Equations of Rotational Kinematics
Example 5 Blending with a Blender
The blades are whirling with an
angular velocity of +375 rad/s when
the “puree” button is pushed in.
When the “blend” button is pushed,
the blades accelerate and reach a
greater angular velocity after the
blades have rotated through an
angular displacement of rad.
The angular acceleration has a
constant value of rad/s2.
Find the final angular velocity of the blades.

12. 8.3 The Equations of Rotational Kinematicsθ α ω ωo t
+44.0 rad
+1740 rad/s2 ?
+375 rad/s

13. 8.4 Angular Variables and Tangential Variables

14. 8.4 Angular Variables and Tangential Variables

15. 8.4 Angular Variables and Tangential Variables

16. 8.5 Centripetal Acceleration and Tangential Acceleration

17. 8.7 The Vector Nature of Angular Variables
Right-Hand Rule: Grasp the axis of rotation with
your right hand, so that your fingers circle the axis
in the same sense as the rotation.
Your extended thumb points along the axis in the
direction of the angular velocity.

18. Problems to be solved
8.31, 8.34, 8.49, 8.62, 8.70, 8.73
B8.1 Convert to degrees (a) 0.1rad (b)π/4rad.Ans: (a) 5.73º (b) 45º
B8.2 Convert to radians (a) 53⁰ (b) 120⁰.
Ans: (a) 0.93rad (b) 2.09rad

19. B8.3 The speeds of centrifuges are limited in part by the strength of the materials used in their construction. A centrifuge spins a 10g sample at a radius of 0.05m at revolutions per minute. (a) What force must the centrifuge exert on the sample? (b) What is the mass of a sample at rest with a weight equal to this force? Ans: (a) N (b) kg

20. B8.4 A centrifuge used to separate blood cells from blood plasma rotates at 55 rotations per second. What is the acceleration at the centre of a centrifuge tube 8.0cm from the axis of rotation?
Ans: 9.55×103m/s2.