Physics 221 Chapter 11 Problem 2 Angular Momentum

Physics 221 Chapter 11

Problem 2. . . Angular Momentum • Guesstimate the formula for the angular momentum? • A. mv • B. m • C. I • D. 1/2 I

Solution 2. . . Angular Momentum • Guesstimate the formula for the angular momentum? • Linear Momentum is mv • Angular Momentum is I

Conservation of Angular Momentum • In the absence of any external torques, the angular momentum is conserved. • If = 0 then I 1 1 = I 2 2

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Problem 3. . . Sarah Hughes • A. When her arms stretch out her moment of inertia decreases and her angular velocity increases • B. When her arms stretch out her moment of inertia increases and her angular velocity decreases • C. When her arms stretch out her moment of inertia decreases and her angular velocity decreases • D. When her arms stretch out her moment of inertia increases and her angular velocity increases

Solution 3. . . Sarah Hughes • B. When her arms stretch out her moment of inertia increases and her angular velocity decreases • I 1 1 = I 2 2 • So when I increases, decreases!

Vector Cross-Product • A X B is a vector whose: • magnitude = |A| |B| sin • direction = perpendicular to both A and B given by the right-hand rule. • Right-hand rule: Curl the fingers of the right hand going from A to B. The thumb will point in the direction of A X B

Torque as a vector Cross-Product =rx. F = r F sin

Angular Momentum L =rx. P L = m v r sin

= d. L/dt Proof L=rxp d. L/dt = d/dt(r x p) d. L/dt = dr/dt x p + r x dp/dt d. L/dt = v x p + r x F But v x p = 0 because p = mv and so v and p are parallel and sin 00 = 0 d. L/dt = r x F = d. L/dt

Problem 4. . . cross product Given: r = 2 i + 3 j and F = - i + 2 j Calculate the torque

Solution 4. . . cross product =rx. F = (2 i + 3 j) x (- i + 2 j) =-2 ixi+4 ixj-3 jxi+6 jxj = 0 + 4 k + 3 k +0 =7 k