Consider a rotating disk of radius R that has the exotic property that it can change its mass per unit area as a function of r. Initially, its mass per unit area is given by ar3, where a is a constant. What is the moment of inertia of this disk expressed in terms of its mass, M and radius R.

A rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the pulsar is 5.00 × 10−4 times the radius of the star before collapse. There is no change in mass. In both cases, the mass of the star is uniformly distributed in a spherical shape.  If the period of the star’s rotation before collapse is 4.00 × 104 s, what is its period after collapse?

Please answer C, D, E The angular position of a rod varies as 20.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at  r1 = 13 cm from the rotation axis and the other at  r2 = 32 cm from the rotation axis. (Note: figure may not be drawn to scale.)   (a) What is the instantaneous angular velocity (in rad/s) of the rod at t = 3 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) 1.24.2 rad/s,  ANSWERED (b) What is the angular acceleration (in rad/s2) of the rod at t = 3 s? (Indicate the direction with the sign of your answer.) 41.4  rad/s2,  ANSWERED (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? vt, 1 =16.146 m/s,  ANSWERED vt, 2 =____m/s  (d)What are the tangential accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.) at, 1 = ______ m/s2 at, 2 = ______ m/s2   (e) What are the centripetal accelerations of the beads at t = 3 s? (Enter the magnitudes…

A 55 kg skater spins at 5 rev / s when her arms are pulled in and at 1 rev / second when her arms are extended. What is the ratio of the skater’s moments of inertia (extended arms / pulled in)?

At latitude 30◦N the distance from the surface of the earth to the axis of rotation,r, is smaller than it is at the equator, by 13% (cos(30◦)≈0.87). If we assume that the angular momentum of a mass m(L=mrv) is conserved as the mass is moved from the equator to latitude 30◦N, how fast is its velocity,v, relative to the ground at 30◦N?

The moment of inertia for a set of objects of mass m; rotating about a common axis is defined as 1 = Σm₁r? 2 where r, is the distance of the ith object to the axis of rotation. If there are many particles that make up a larger object then this sum transforms into an integral, 4-fff or a. I = dV, V where p is the mass density and V the volume of the object. In this exercise we will explore moment of inertia by rolling two objects down an incline plane in the Experimental Math Lab Space.

A 2.5 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 540 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpm, just after this event?

Answer D, E, & F: Given that a) M*Vd b) M*V^2 C) M*Vd ( angular momentum is conserved)

A child's top is held in place upright on a frictionless surface. The axle has a radius of r 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R SP 9.15 x10¬3 kg-m² L = S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T 2r T 2.42 x10-4 kg-m? = Incorrect

0.1/1E: In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that-is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T in the cord at the left and (c) the tension T2 in the cord at the right. %3D %3! R. (a) Number i Units m/s^2 (b) Number i Units (c) Number Units eTextbook and Media 898 MAY 1 PDF 8 tv .. DD 80 000 000 888 F9 F10 F11 F6 F7 FB F2 F3 F4 F5 @ 23 2$ & 2 3 4 7 8 9