Calculating Moment of Inertia The squared distance from each point mass to the axis is Using the Pythagorean Theorem s0/=m=m2+m+m2+m=4m 1= 2mL2 L2 m● m m m Physics 121: Lecture 18, Pg 6
Physics 121: Lecture 18, Pg 6 Calculating Moment of Inertia... The squared distance from each point mass to the axis is: m m m m L r L/2 2 L 2 L r 2 2 2 2 = = 2 L 4m 2 L m 2 L m 2 L m 2 L I m r m 2 2 2 2 2 N i 1 2 = i i = + + + = = so I = 2mL2 Using the Pythagorean Theorem
Calculating Moment of Inertia Now calculate /for the same object about an axis through the center, parallel to the plane(as shown) =∑mr=m+m+m+m==4m I= ml2 m m m● Physics 121: Lecture 18, Pg 7
Physics 121: Lecture 18, Pg 7 Calculating Moment of Inertia... Now calculate I for the same object about an axis through the center, parallel to the plane (as shown): m m m m L r 4 L 4m 4 L m 4 L m 4 L m 4 L I m r m 2 2 2 2 2 N i 1 2 = i i = + + + = = I = mL2
Calculating Moment of Inertia Finally, calculate / for the same object about an axis along one side(as shown) =∑mr2=ml2+m2+m02+m0 1= 2mL2 m m Physics 121: Lecture 18, Pg 8
Physics 121: Lecture 18, Pg 8 Calculating Moment of Inertia... Finally, calculate I for the same object about an axis along one side (as shown): m m m m L r 2 2 2 2 N i 1 2 I = mi r i = mL + mL + m0 + m0 = I = 2mL2
Calculating Moment of Inertia. For a single object, I clearly depends on the rotation axis 1= 2mL2 ml 1= 2mL2 m m● m Physics 121: Lecture 18, Pg 9
Physics 121: Lecture 18, Pg 9 Calculating Moment of Inertia... For a single object, I clearly depends on the rotation axis !! L I = 2mL2 I = mL2 m m m m I = 2mL2
Lecture 18. Act 1 Moment of Inertia a triangular shape is made from identical balls and identical rigid, massless rods as shown the moment of inertia about the a, b, and c axes is la, Ib, and Ic respectively Which of the following is correct (a)12>1b>1c (b)la>Ic>Ib (c)b>a>Ic abc Physics 121: Lecture 18, Pg 10
Physics 121: Lecture 18, Pg 10 Lecture 18, Act 1 Moment of Inertia A triangular shape is made from identical balls and identical rigid, massless rods as shown. The moment of inertia about the a, b, and c axes is Ia , Ib , and Ic respectively. Which of the following is correct: (a) Ia > Ib > Ic (b) Ia > Ic > Ib (c) Ib > Ia > Ic a b c