A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r,...

A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r, and a hollow cylinder of radius r are all allowed to roll down an incline. Derive a general relationship for the linear acceleration of each object depending on the angle of the ramp and the rotational inertia. You may assume that the frictional force is small enough that it is only causing rotation in each case.

Expert Solution

genius_generous answered 1 year ago

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder...

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder of radius R all have the same mass, and all three are rotating with the same angular velocity. The sphere is rotating around an axis through its center, and each cylinder is rotating around its symmetry axis. Which one has the greatest rotational kinetic energy? both cylinders have the same rotational kinetic energy the solid cylinder the solid sphere they all have the same...

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius....

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius. They both roll without slipping, have the same linear speed and approach the same inclined plane. As they roll up the inclined plane, they continue to roll without slipping. Which object will reach the greatest height on the inclined plane? A: solid homogeneous cylinder B: solid homogeneous sphere C: they both reach the same maximum height If you could explain why in your answer...

A frictionless pulley, which can be modeled as a 0.90kg solid cylinder with a 0.31m radius

A frictionless pulley, which can be modeled as a 0.90kg solid cylinder with a 0.31m radius, has a rope going over it, as shown in the figure. The tensions in the rope are 12N and 10N. What is the angular acceleration of the pulley?

(a) Plot the electric field of a charged conducting solid sphere of radius R as a...

(a) Plot the electric field of a charged conducting solid sphere of radius R as a function of the radial distance r, 0 < r < 1, from the center. (b) Plot the electric field of a uniformly charged nonconducting solid sphere of radius R as a function of the radial distance r, 0 < r < 1, from the center.

A solid sphere of charge is centered at the origin and has radius R = 10...

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Suppose a solid cylinder of radius R is caused to rotate with a torque of known...

Suppose a solid cylinder of radius R is caused to rotate with a torque of known magnitude about an axis through its center. The same torque is then applied to a hollow cylinder of outer radius R and inner radius r. If their masses are equal, which object has the greater angular acceleration? A. The solid cylinder has greater angular acceleration. B. Both cylinders have the same acceleration C. The hollow cylinder has a grater angular acceleration

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform...

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density ρ0, and the “southern” hemisphere a uniform charge density −ρ0. Find the approximate field E(r,θ) for points far from the sphere (r ≫ R). P.S. Please be as neat as possible.

A solid insulating sphere of radius R has a charge of Q, (Q > 0) placed...

A solid insulating sphere of radius R has a charge of Q, (Q > 0) placed on it, uniformly distributed throughout its volume. Surrounding the sphere is a spherical conducting shell with inner radius 2R and outer radius 3R and has a charge of −2Q placed on it. The sphere and the shell share the same center. 1A: Determine the magnitude of the electric field, E(r), where r is the distance from the center of the sphere 1B: Determine the...

A solid nonconducting sphere of radius R = 5.5 cm has a nonuniform charge distribution of...

A solid nonconducting sphere of radius R = 5.5 cm has a nonuniform charge distribution of volume charge density ρ = (15.4 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/2.0, and (d) r = R?

A solid sphere of radius R is found at the origin. Point mass particles m have...

A solid sphere of radius R is found at the origin. Point mass particles m have elastic collisions with the sphere. Find a relationship between the (scattering) angle and the impact parameter to calculate the differential (cross-section) and the total differential.

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