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Lesson 11: Angular Motion, image, image, image, image, image, image, image…
Lesson 11: Angular Motion
Angular Terms
Angular Displacement
Defined as the angle and the direction through which a body turns
Measured using rad or revolution
Denoted by theta
Important note: 1 revolution (1 turn) = 360 degrees = 2pi radians
Angle in radians
Ratio of two lengths
Pure number, which means there is no dimensions
Angular Velocity
Defined as the rate of change of angular displacement with respect to time
Angular velocity (Mathematical form):
Measured using radians per second [rad/s]
Can also be represented as revolution per minute [rpm]
Important thing to note: 1 rpm = 2pi/60 rad/s
Angular Acceleration
Defined as the rate of change of angular velocity with respect to time
Angular Acceleration (Mathematical form):
Measured using radians per second squared [rad/s2]
Uniform Motion
A motion when the angular acceleration is constant
Three equations of rotational motion with constant angular acceleration are:
Important Formulas
Comparison of Linear and Rotational Motion Equations (Uniform Motion) with Constant Acceleration:
RELATIONSHIP between LINEAR and ANGULAR Motion:
Normal or Centripetal Acceleration
For a body moving in a circular motion
Have an acceleration an, that is radially inwards towards the centre of the circle with a magnitude given by
Important Note: To find the total acceleration of acceleration and tangential acceleration:
Translational Motion & Rotational Motion
Translational Motion
For a rolling ball,
Every particle in the rigid body has the same instantaneous velcocity
Means that there is no rotation
Rotational Motion
For a rolling ball,
Every particle in the rigid body has the same angular velocity
Also travels in circles around a fixed axis
Rolling Motion
Combination of Translational and Rotational Motion
Translational Motion vs Rotational Motion
Rotational Motion: Motion about a fixed axis, all the particles have the same instantaneous angular velocity and travel in circles about the axis of rotation
General Rigid-body motion: A combination of TRANSLATIONAL and ROTATIONAL motion
Common example: Rolling
Combination of both TRANSLATIONAL and ROTATIONAL motion of a rigid body
Rolling without SLIPPING is a combination of ROTATION and TRANSLATION
Point of contact is instantaneously at rest, point 3 at the top of the wheels moving forward twice as fast as the center of mass; points 2 and 4 at the side have velocities at 45 degrees to the horizontal.
