I'm trying to understand the difference between a solid sphere rotating with the axis through its...
I'm trying to understand the difference between a solid sphere rotating with the axis through its center versus a solid sphere rotating and the axis tangent to the surface.
I'd like help in having some examples so I can understand what moment of inertia to use when. For instance, if a solid sphere is rotating down a frictionless incline, would I use the first option because the sphere is rotating around it's own axis?
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I'm trying to understand the difference between a solid sphere
rotating with the axis through its...
A uniform solid sphere has a moment of inertia I about an axis tangent to its...
A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?
5. A uniform solid sphere rolls without slipping down a 19° inclined plane. What is the...
5. A uniform solid sphere rolls without slipping down a 19° inclined plane. What is the acceleration of the sphere's center of mass? The moment of inertia of a uniform solid sphere about an axis that passes through its center = ⅖mr². The moment of inertia of a uniform solid sphere about an axis that is tangent to its surface = 7⁄5mr².
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its fi...
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its final position at the bottom of the incline. a) Find the velocity of the ball at the bottom of the ramp in terms of m, r, d, 8, and g. The moment of inertia of a sphere...
A solid cylindrical disk with moment of inertia I, rotates about a vertical axle through its center with angular ve...
A solid cylindrical disk with moment of inertia I, rotates about a vertical axle through its center with angular velocity o;. A second, smaller solid cylindrical disk with moment of inertia 12 , which is not rotating, is dropped onto the first disk. Shortly after the collision, the two disks reach a common final angular velocity of. Assume the axle is frictionless. Before After 1 INI i - II II - 1 Find an expression for of in terms of...
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass.
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass. The axis is perpendicular to the disk. The moment of inertial for the disk with a central axis is I MR2. Two non-rotating smaller disks, each with mass M2 and radius R/4, are glued on the original disk as shown in the figure. (a) Show that the ratio of the moments of inertia is given by I'/I = 35/16, where I' is the moment...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia I_t rotating at a constant angular velocity omega_i around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so...
positive direction) Multiple Choice 15% each! 1. A solid uniform sphere of mass 1.85 kg and...
positive direction) Multiple Choice 15% each! 1. A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 revisit stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is dosest to (A) 0.0466 Nm (B) 0.00593 Nm (C) 0.0620 Nm (D) 0.149 Nm (E) 0.0372 Nm 2. If the torque on an object...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. (...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. (Figure 1) Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity ωi around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is...
A moon of mass m orbits around a non-rotating planet of mass M with orbital angular velocity . The moon also rotates about its own axis with angular velocity .
1. A moon of mass \(m\) orbits around a non-rotating planet of mass \(M\) with orbital angular velocity \(\Omega\). The moon also rotates about its own axis with angular velocity \(\omega\). The axis of rotation of the moon is perpendicular to the plane of the orbit. Let \(I\) be the moment of inertia of the moon about its own axis. You can assume \(m<<M\)so that the center ofmass of the system is at the center of the planet.(a) What is...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere be Isphere. A massless cord passes around the equator of the sphere, over a pulley with rotational inertia I pulley and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. At t = 0, the mass...
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its final position at the bottom of the incline. a) Find the velocity of the ball at the bottom of the ramp in terms of m, r, d, 8, and g. The moment of inertia of a sphere...
A solid cylindrical disk with moment of inertia I, rotates about a vertical axle through its center with angular velocity o;. A second, smaller solid cylindrical disk with moment of inertia 12 , which is not rotating, is dropped onto the first disk. Shortly after the collision, the two disks reach a common final angular velocity of. Assume the axle is frictionless. Before After 1 INI i - II II - 1 Find an expression for of in terms of...
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia I_t rotating at a constant angular velocity omega_i around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so...
positive direction) Multiple Choice 15% each! 1. A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 revisit stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is dosest to (A) 0.0466 Nm (B) 0.00593 Nm (C) 0.0620 Nm (D) 0.149 Nm (E) 0.0372 Nm 2. If the torque on an object...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere be Isphere. A massless cord passes around the equator of the sphere, over a pulley with rotational inertia I pulley and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. At t = 0, the mass...
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