Solid, uniform cylinder of mass m and radius R is fitted with a frictionless axle along the cylinder's long axis. A horizontal spring (spring constant k) is attached to this axle. Under the influence of the spring, the cylinder rolls back and forth without slipping on a horizontal surface. What is the frequency of this motion?

A block of mass is attached to the end of an ideal spring. Due to the weight of the block, the block remains at rest when the spring is stretched a distance from its equilibrium length. The spring has an unknown spring constant.
A. What is the spring constant?
B. Suppose that the block gets bumped and undergoes a small verti

2) A force Fext(t) = F0[ 1?exp(?((alpha)(t)) ] acts, for time t > 0, on an oscillator which is at rest at x=0 at time 0. The mass is m; the spring constant is k; and the damping force is ?b[(x)dot]. The parameters satisfy these relations:
b = m*q , k = 4*m*q^2 (where q is a constant with units of inverse time)

A 5.0 kg block hangs from a spring with spring constant 2000 N/m. The block is pulled down 5.0 cm from the equilibrium position and given an initial velocity of 1.0 m/s back toward equilibrium. What are (a) the frequency, (b) amplitude, (c) phase constant and (d) the total mechanical energy of the motion (e) write the equation

One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x=0. The length of the relaxed spring is L... (see attached)
Please do not place your

An ice skater has a moment of inertia of 5.0 kg-m^2 when her arms are outstretched. At this time, she is spinning at 3.0 revolutions per second. If she pulls her arms in, she decreases her moment of inertia to 2.0 kg-m^2. How fast is she spinning then?
Please provide detailed explanation.

Two disks are rotating about the same axis. Disk A has a moment of inertia of 8.86 kg·m2 and an angular velocity of +8.31 rad/s. Disk B is rotating with an angular velocity of -9.45 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single unit with an angular velocit

1. If a net torque is applied to an object, that object will experience which of the following?
a. constant angular velocity
b. an angular acceleration
c. a constant moment of inertia
d. an increasing moment of inertia.
2. A grinding wheel with moment of inertia of 2.0 kg.m2 is initially at rest. What angular momentum wi

Please help with the following problem. Provide step by step calculations fo reach.
A uniform cylinder (A) has a mass ( m = 3 kg ), radius ( r = 150 mm ), and can roll without sliding on a cart ( C ) of mass ( M = 5 kg ). Cylinder (A) is attached to a spring (AB) of stiffness (constant) k = 100 N/m as shown (attached). The s

A large turntable rotates about a fixed vertical axis, making one revolution in a time of T. The moment of inertia of the turntable about this axis is I. A child with a mass of m, initially standing at the center of the turntable, runs out along a radius.
What is the angular speed of the turntable when the child is a distance