King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 35

Objective Moment of Inertia of a body Parallel Axis Theorem Radius of Gyration Moment of Inertia of Composite Bodies

Parallel Axis Theorem The moment of inertia about any axis parallel to and at distance d away from the axis that passes through the centre of mass is: Where –I G = moment of inertia for mass centre G –m = mass of the body –d = perpendicular distance between the parallel axes.

Radius of Gyration

Mass Center Example

Objectives Apply the Equation of Translation motion –Rectilinear Translation –Curvilinear Translation Apply the equation of Rotation motion The roll of the center of mass G Discuss the slipping Vs. Tipping Discuss the slipping Vs. freely rotating Discuss the “wheely” Vs. Non-wheely

General Application of the Equations of Motion Summation of moment in FBD = summation of the kinetic moment in K.D

Rectilinear Translation

Curvilinear Translation

Discuss the slipping Vs. Tipping x N If x > 1.5 ft tipping If x < 1.5 ft slipping

Slipping Vs. Freely rotating FA=sNAFA=sNA NANA NBNB mg

“Wheely” Vs. Non-Wheely N B =0 Wheely : lift the front wheel off the ground

Example 17-5

Example 17-8 m BD =100kg m AB =m CD = Neglect  = 30 o  = 6 rad/s T A = ? T B = ? a G =?

Problem m= 80 kg  B =0.8 N A =? N B =? When rear wheel locks for break a =? Deceleration NANA NBNB BNBBNB aGaG

Problem m= 80 kg  B =0.8 N A =? N B =? a =? When traveling at constant velocity and no break was applied NANA NBNB BNBBNB a = 0

Problem m= 80 kg N A =? N B =? a =?  k =? minimum When rider applies the front break and back wheel start to lift off the ground NANA N B =0 kNAkNA

Rotation About a Fixed Axis

Pin Reaction Horizontal Reaction Vertical Reaction OR Normal Reaction Tangential Reaction OtOt OnOn OyOy OxOx OnOn OtOt

Example 17-9 Start from rest  =? Number  =20rad/s Pine reaction

Example 17-10

Example m=60 kg Radius of gyration k O =0.25 m b =20 kg  =? Drum a=?

Example W=50 Ib k G =0.6 ft  = 8 rad/s Pin reaction =?

Frictional Rolling Problems - rolls without slipping - slides as it rolls

Example m = 8 Kg radius of gyration k G =0.3m.  =?.

W= 50-lb radius of gyration k G =0.70ft. a G =?. Example 17-15

Example m=100 kg I G =75 kg.m 2  =? The pole at rest

Example 17-17