Physics 3210Week 11 clicker questionsMultiplication of a vector by a matrix A is a linear transformationWhat happens to an eigenvector of A under this linear transformation (assuming the corresponding eigenvalue is nonzero)?A. The magnitude of the vector can change, but not its direction.B. The direction of the vector can change, but not its magnitude.C. Both the magnitude and the direction of the vector can change.D. Neither the magnitude nor the direction of the vector can change.AvvThe eigenvalue equation can be written asWhat condition must be satisfied for l to be an eigenvalue of A?A. B. C. D.  AIl v0 A I 0l  det A I 0l  det A 0A v0The matrix A has eigenvectorswhich correspond to eigenvaluesThe matrix S has the eigenvectors as its columns: What is the product AS?A. B. C. D. 1 2 nv v v,,1 2 nSv v v1 1 1 2 1 nAS l l lv v v1 2 nl l l,,1 2 nAS A A Av v v1 1 2 2 n nAS l l lv v vT11T22TnnASl llvvvWhich of the following is the correct description of a cube of constant density?A. Spherical top. B. Oblate symmetric top. C. Prolate symmetric top.D. Asymmetric top. E. Rotor.Physics 3210Wednesday clicker questionsHow is the time derivative of a vector v in an inertial frame (I) related to the time derivative of the vector in a rotating frame (R), which rotates with angular velocity vector ω?A. B. C. D. IRdddt dtvvIRdddt dtvvωIRdddt dt  vvωvIRdddt dt  vvv ωWhat is the first component of ωxIω?A. B. C. D. E. 2 3 3 2II   2 3 2 3II   1 3 3 1II   1 3 1 3II   1 2 2 1II  A rotating dumbbell consists of two masses (mass m) which move in circles (radius a) at z displacement ℓ and -ℓ, joined by a massless rod. The angular velocity vectorConsider the body frame where the positions of the masses are (0,a,ℓ) and (0,-a,-ℓ). What are the principle axes of inertia? ℓωzˆωaxyzA. C.v1v2v3v1v2v3v1v2v3B. D. v1v2v3A rotating dumbbell consists of two masses (mass m) which move in circles (radius a) at z displacement ℓ and -ℓ, joined by a massless rod. The angular velocity vectorConsider the body frame aligned with the principle axes of inertia (as sketched). What are the components of the angular velocity vector in this frame? ωzˆωA.B. v1v2v3θsincos0  ωsin0cosωC.D. cossin0  ωcos0sinωA rotating dumbbell consists of two masses (mass m) which move in circles (radius a) at z displacement ℓ and -ℓ, joined by a massless rod. The angular velocity vectorConsider the body frame aligned with the principle axes of inertia (as sketched). What are Euler’s equations in this frame? ωzˆωA.B. v1v2v3θ123000C.D.  122 2 23002m a sin cos     ℓa 122 2 23002m a sin     1222 2 2302ma2m a sin      A rotating dumbbell consists of two masses (mass m) which move in circles (radius a) at z displacement ℓ and -ℓ, joined by a massless rod. The angular velocity vectorConsider the body frame aligned with the principle axes of inertia (as sketched). In this frame, the torque is constant in the 3 direction (out of the page). How can you describe the torque in the space frame? ωzˆωA. The torque is zero.B. The torque is constant, in the same direction as in the body frame.C. The torque rotates with a constant angular velocity about the z axis.D. The torque rotates with a constant angular velocity about the x axis.E. The torque rotates alternately about the z and x axes.v1v2v3θℓaxyzA rotating dumbbell consists of two masses (mass m) which move in circles (radius a) at z displacement ℓ and -ℓ, joined by a massless rod. The angular velocity vectorConsider the body frame aligned with the principle axes of inertia (as sketched). What is the angular momentum in this frame? ωzˆωA.B. v1v2v3θC.D. ℓa 2202m a sin0   L  222m a sin00  L02ma sin0  L 2ma sin00LPhysics 3210Friday clicker