In Fig. 15-59, a solid cylinder attached to a horizontal spring ( k = 3.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these conditions the cylinder's center of mass executes simple harmonic motion with period T = 2 π 3 M 2 k , where M is the cylinder mass. ( Hint: Find the time derivative of the total mechanical energy.) Figure 15-59 Problem 100.
In Fig. 15-59, a solid cylinder attached to a horizontal spring ( k = 3.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these conditions the cylinder's center of mass executes simple harmonic motion with period T = 2 π 3 M 2 k , where M is the cylinder mass. ( Hint: Find the time derivative of the total mechanical energy.) Figure 15-59 Problem 100.
In Fig. 15-59, a solid cylinder attached to a horizontal spring (k = 3.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these conditions the cylinder's center of mass executes simple harmonic motion with period
T
=
2
π
3
M
2
k
,
where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.)
Figure 15-59 Problem 100.
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
A solid sphere, made of acrylic plastic with a density of 1.1 g/cm3,1.1 g/cm3, has a radius of 5.0 cm.5.0 cm. A very small "eyelet" is screwed into the surface of the sphere and a horizontal support rod is passed through the eyelet, allowing the sphere to pivot around this fixed axis, as shown in the figure. If the sphere is displaced slightly from equilibrium on the surface of Earth, determine the period ?T of its harmonic motion when it is released.
The moment of inertia of a physical pendulum of 3 kg oscillating at small angles around an axis at a distance h = 0.8 m from the center of mass is given as I = 1.2 kg m ^ 2. What should be the length of a simple pendulum with a mass of 0.8 kg oscillating in the same period as the small oscillations of the pendulum? bIf the swing amplitude is 0.5 rad, what is the maximum value of the angular acceleration? (a-10rad/S b-20rad/s c-1/10rad/s d-20rad/S). (
figure for first question)
A physical pendulum consisting of a uniform solid disk of mass 563 g and radius 14.4 cm supported in a vertical plane by a pivot located a distance 10.2 cm from the center of the disk . The disk is displayed by a small angle and released . Find the period of the resulting SHM ?
Sears And Zemansky's University Physics With Modern Physics
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.