Chapter 7Chapter 7 Rotational Motion & Law of Rotational Motion & Law of

GravityGravity

Section 7-2Section 7-2

Tangential and Centripetal Tangential and Centripetal AccelerationAcceleration

Tangential SpeedTangential Speed

Objects in circular motion have Objects in circular motion have tangential speed.tangential speed.

Tangential SpeedTangential Speed of any point of any point rotating about an axis is rotating about an axis is instantaneous linear speedinstantaneous linear speed of that of that point.point.

Example: Tangential SpeedExample: Tangential Speed

Horses on a carousel move at the Horses on a carousel move at the same same angular angular speedspeed but but differentdifferent tangential speedstangential speeds..

Tangential SpeedTangential Speed

Tangential Speed = distance from Tangential Speed = distance from axis x angular speed.axis x angular speed.

VVtt = r = r ωω

Where Where rr is Radius and is Radius and ωω is is instantaneous angular speed (speed instantaneous angular speed (speed at that moment)at that moment)

Practice with Sample 7EPractice with Sample 7E

Pg. 255Pg. 255

Tangential AccelerationTangential Acceleration

Tangential Acceleration is tangent to Tangential Acceleration is tangent to the circular path.the circular path.

Tangential acceleration = distance Tangential acceleration = distance from axis x angular accelerationfrom axis x angular acceleration

aatt = r = r αα

Where Where r r is Radius and is Radius and αα is is instantaneous angular acceleration.instantaneous angular acceleration.

Practice with Sample 7FPractice with Sample 7F

Pg. 256Pg. 256

Centripetal AccelerationCentripetal Acceleration

‘‘Center seekingCenter seeking’ acceleration.’ acceleration.

Circular motion Circular motion accelerationacceleration is due to is due to change in direction.change in direction.

Example: Centripetal AccelerationExample: Centripetal Acceleration

Tangential and Centripetal accelerations Tangential and Centripetal accelerations are are perpendicular.perpendicular.

Tangential Vs. Centripetal Tangential Vs. Centripetal AccelerationAcceleration

Tangential and Centripetal Tangential and Centripetal accelerations are accelerations are not the samenot the same..

TangentialTangential Component of acceleration Component of acceleration is due to is due to changing speed.changing speed.

Centripetal Centripetal component of acceleration component of acceleration is due to is due to changing direction.changing direction.

Formula: Centripetal AccelerationFormula: Centripetal Acceleration

Centripetal Acceleration = Centripetal Acceleration = (tangential speed)(tangential speed)2 2 / distance from / distance from axisaxis

aacc = v = vtt22 / r / r

aacc = r = r ωω22

Sample Problem 7GSample Problem 7G

Pg. 258Pg. 258

AssignmentAssignment

Practice 7E pg. 255 2-4Practice 7E pg. 255 2-4 Practice 7F pg. 256 2-3Practice 7F pg. 256 2-3 Practice 7G 2-5Practice 7G 2-5

Eight problems Total!!Eight problems Total!!