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4) A solid uniform sphere mass M an radius R pivots around its center, which is...
(11 points) A uniform solid sphere of mass m and radius r is placed inside a...
(11 points) A uniform solid sphere of mass m and radius r is placed inside a hemispherical bowl of radius R. The sphere is released from rest at an angle theta and rolls without slipping. (a) (6 points) Using Conservation of Energy, to find an expression for the angular speed of the sphere when it reaches the lowest point of the bowl. (b) (6 points) Find the magnitude of the centripetal acceleration of the center of mass of the sphere...
Q3-(25 pts) A pulley of mass Mand radius R can rotate around its center of mass...
Q3-(25 pts) A pulley of mass Mand radius R can rotate around its center of mass freely. Take the moment of inertia of the pulley as 1o. A string with negligible mass is wrapped around the pulley. One end of the string holds a block with mass m and the other end is attached to a spring with a force constant k. Assume no friction at any surface and string is not slipping on pulley. a) When the system is...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ens...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
A uniform solid sphere with a mass M = 2.0 kg and a radius R =...
A uniform solid sphere with a mass M = 2.0 kg and a radius R = 0.10 m is set into motion with an angular speed ωo = 70 rad/s. At t = 0 the sphere is dropped a short distance (without bouncing) onto a horizontal surface. There is friction between the sphere and the surface. Find (a) the angular speed of rotation when the sphere finally rolls without slipping at time t = T and (b) the amount of...
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.
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
A uniform, solid sphere of radius 5.00 cm and mass 1.75 kgstarts with a purely translational...
A uniform, solid sphere of radius 5.00 cm and mass 1.75 kgstarts with a purely translational speed of 3.25 m/s at the top of an inclined plane. The surface of the incline is 1.75 m long, and is tilted at an angle of 24.0∘with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed ?2at the bottom of the ramp.
A uniform, solid sphere of radius 5.00 cm and mass 4.75 kg starts with a purely...
A uniform, solid sphere of radius 5.00 cm and mass 4.75 kg starts with a purely translational speed of 1.75 m/s at the top of an inclined plane. The surface of the incline is 1.50 m long, and is tilted at an angle of 26.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed ?2 at the bottom of the ramp. ?2=
A uniform, solid sphere of radius 4.00 cm and mass 2.25 kg starts with a purely...
A uniform, solid sphere of radius 4.00 cm and mass 2.25 kg starts with a purely translational speed of 2.25 m/s at the top of an inclined plane. The surface of the incline is 1.75 m long, and is tilted at an angle of 33.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed ?2 at the bottom of the ramp.
A uniform, solid sphere of radius 4.25 cm and mass 2.00 kg starts with a purely...
A uniform, solid sphere of radius 4.25 cm and mass 2.00 kg starts with a purely translational speed of 1.00 m/s at the top of an inclined plane. The surface of the incline is 1.00 m long, and is tilted at an angle of 22.0" with respect to the horizontal Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speedy at the bottom of the ramp.v2 = _______ m/s
(11 points) A uniform solid sphere of mass m and radius r is placed inside a hemispherical bowl of radius R. The sphere is released from rest at an angle theta and rolls without slipping. (a) (6 points) Using Conservation of Energy, to find an expression for the angular speed of the sphere when it reaches the lowest point of the bowl. (b) (6 points) Find the magnitude of the centripetal acceleration of the center of mass of the sphere...
Q3-(25 pts) A pulley of mass Mand radius R can rotate around its center of mass freely. Take the moment of inertia of the pulley as 1o. A string with negligible mass is wrapped around the pulley. One end of the string holds a block with mass m and the other end is attached to a spring with a force constant k. Assume no friction at any surface and string is not slipping on pulley. a) When the system is...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
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