Consider the motion of a rigid body with principal moments of inertia I < I<I,, in...
4) A rigid body rotates with constant angular velocity about a fixed axis. Show that its kinetic energy K and angular momentum L are related according to K = 5, where I is the rotational inertia.
3. Consider a rigid rotor whose Hamiltonian is given by H L2(21) where L is the angular momentum operator and I is the moment of inertia of the rotator. Its rotation is described by a wave function: (0, N{Yo0(0,6)(1 3i) Y1-1(0,6) 2 Y21(0.0) Y20(0.) Find the normalization constant, N. (i) Find the probability to occupy state Yo0- (ii Find the expectation value of L2 of this state (iii Find the expectation value of L2 of this state (iv) Find (L2L2/21...
Consider the simplest rigid body, consisting of two point objects each of mass m, connected by a massless stick of length 2f. Suppose that the motion of this baton is to spin about an axis we'll choose to call , i.e. w = w2. We choose our origin at the center of mass, which is stationary. The angle between the AB axis and i is B. 6. Express in the êk basis. Likewise, express the system's angular momentum L, and...
A Review Learning Goal: To apply the principle of work and energy to a rigid body. Submit Previous Answers Correct Part B The principle of work and energy is used to solve kinetic problems that involve velocities, forces, moments, and displacements. For a rigid body, the principle is Ti + QU1–2 = T2 where Ti is the body's initial kinetic energy, EU1-2 is the work done by external forces and moments that act on the body, and T2 is the...
4. (Rigid body rotation) A blob is made from four small objects of mass m attached together with massless bars of length l. The angle made by the bars is 45 degrees. A Identify the principle axes for this blob. B Using a coordinate system, the body frame, that corresponds to those axes, determine the intertia tensor for rotation about the center point. C Suppose that the blob is floating in space, with no torques applied, and is rotating with...
point p lies in a rigid body that rotates at angular velocity, ω-i 7-j 10-k 5 and angular acceleration, α itj 12-k 9. The body rotates about fixed point 0, and the radius vector op is given by R-i 3-j 8-k 2. Find e acceleration of P using cross product, Unit vector i,j, and k lie in a fized coordinate system. (11 points) (a) If
We know the heart shaped object has a moment of inertia of I = 0.5kgm^2. Calculate the change in angular momentum (L) of the object in 5s (~L=~τ∆t). This question deals with angular momentum conservation. Two girls of mass 100 kg each stand at the center of a rotating merry-go-round (MGR) in the shape of a disk of radius 1 m and mass 10 kg. The platform rotates atω= 0.40 rad/s. Let’s call this configuration instant A. A) Determine the...
1.) For a rotating rigid body which of the following statements is not correct? a.) all points along a rotating rigid body move with constant speed b.) points along a rotating body move through the same angle in equal time intervals c.) point along a rotating body have velocities that continuously change directions d.) all of the above 2.) Which of the following quantities will impact how a rigid body's rotational speed can change? a.) the body's rotational inertia b.)the...
037 CH 19.2 1 of 4> Principle of Impulse and Momentum Constants Part A - Angular velocity of the pulley Learning Goal The pulley shown (Figure 1) has a moment of inertia IA 0.900 kg m2, a radius r 0.300 m, and a mass of 20.0 kg A cylinder is attached to a cord that is wrapped around the pulley. Neglecting bearing friction and the cord's mass express the pulley's final angular velocity in terms of the magnitude of the...