Physics Rotational Mechanics Level: High School
The three sphere in the figure at “click here” , with masses m1 = 765 g, m2 = 85g , and m3 = 245 g , have their centers on a common line , with L = 12 cm and d = 4.0 cm . You move the middle sphere until its center-to-center separation from m3 is d = 4.0 cm .(a) How much work is done on m2 by you ?
Physics Rotational Mechanics Level: High School
A planet moves in an elliptical orbit about a star under the action of gravitational forces .A) List the converved quantities of the system .
B) Suppose the closet approach the planet makes to the star occurs at A , a distance of 10^7 meters and the furthermost approach occurs at B a distance of 3*10^7 meters . If the planet speed at A is 10^4 m/s What is its velocity at B ?
Physics Rotational Mechanics Level: High School
A square object with a circle cut in its center spins about its center of mass , with radius R . The object has mass M and the length of the edge of the square is 2R . What is the moment of inertia for this object ?An early invention was a steam apparatus made from a cauldron that contained water heated by fire . The steam was fed up into a hollow spherical container with two spouts on each side . When the steam exited it would spin the container at high speeds . The spherical container has a radius of 0.20m and mass of 10kg . The two spouts are massless , but extend an additional 0.10m above the surface of the container . The container is hollow , and the moment of inertia of the steam inside is not considered .
Explain the full energy cycle of this problem , beginning with where it comes from and explain its transformation into other forms of energy .
Physics Rotational Mechanics Level: High School
A square object with a circle cut in its center spins about its center of mass , with radius R . The object has mass M and the length of the edge of the square is 2R . What is the moment of inertia for this object ?An early invention was a steam apparatus made from a cauldron that contained water heated by fire. The steam was fed up into a hollow spherical container with two spouts on each side . When the steam exited it would spin the container at high speeds . The spherical container has a radius of 0.20m and mass of 10kg . The two spouts are massless , but extend an additional 0.10m above the surface of the container . The container is hollow , and the moment of inertia of the steam inside is not considered .
How long does it take for the sphere to get to the maximum angular speed found above ?
Physics Rotational Mechanics Level: High School
A square object with a circle cut in its center spins about its center of mass , with radius R . The object has mass M and the length of the edge of the square is 2R . What is the moment of inertia for this object ?An early invention was a steam apparatus made from a cauldron that contained water heated by fire . The steam was fed up into a hollow spherical container with two spouts on each side . When the steam exited it would spin the container at high speeds . The spherical container has a radius of 0.20m and mass of 10kg . The two spouts are massless , but extend an additional 0.10m above the surface of the container . The container is hollow , and the moment of inertia of the steam inside is not considered .
If the energy contained with in the spherical container is completely converted to rotational kinetic energy , it will yield an estimate of the maximum rotation rate of the vessel . What is this maximum value ?
Physics Rotational Mechanics Level: High School
A square object with a circle cut in its center spins about its center of mass , with radius R . The object has mass M and the length of the edge of the square is 2R . What is the moment of inertia for this object ?An early invention was a steam apparatus made from a cauldron that contained water heated by fire . The steam was fed up into a hollow spherical container with two spouts on each side . When the steam exited it would spin the container at high speeds . The spherical container has a radius of 0.20m and mass of 10kg . The two spouts are massless , but extend an additional 0.10m above the surface of the container . The container is hollow , and the moment of inertia of the steam inside is not considered .
If the pressure inside reaches 1.5 atmospheres what is the angular acceleration of the container? The area of the spouts are circles of radius 0.010m, and outside pressure is 1 atmosphere .
Physics Rotational Mechanics Level: High School
A square object with a circle cut in its center spins about its center of mass , with radius R . The object has mass M and the length of the edge of the square is 2R . What is the moment of inertia for this object ?An early invention was a steam apparatus made from a cauldron that contained water heated by fire . The steam was fed up into a hollow spherical container with two spouts on each side . When the steam exited it would spin the container at high speeds . The spherical container has a radius of 0.20m and mass of 10kg . The two spouts are massless , but extend an additional 0.10m above the surface of the container . The container is hollow , and the moment of inertia of the steam inside is not considered .
What is the moment of inertia of the container ?
Physics Rotational Mechanics Level: High School
A block of mass m slides at speed v on a frictionless surface and strikes a previously stationary block of mass 4m which is attained to a spring of constant k . After collision the first block bounces back to left at a speed v/3 . Find the maximum compression.
Physics Rotational Mechanics Level: High School
A particle of mass M is moving on a frictionless horizontal table and is attached to a massless string whose other end passes through a hole in the table where I am holding it . Initially particle is moving in a circular of radius r_0 with angular velocity w_0 but I now pull the string down through the hole until a length r remains between the hole and particle , What is the particle angular velocity now ?
Assume that I pull the string so slowly that we can approximate the particles path by a circle of slowly shrinking radius , calculate the work I did pulling the string and compare this answer with the particles gain in Kinetic energy ?
Physics Rotational Mechanics Level: High School
Calculate the x and y coordinates of the center of mass of the following object . Assume the object is of uniform mass density .
Physics Rotational Mechanics Level: High School
A tennis ball is a hollow sphere with a thin wall . It is set rolling without slipping at 4.03 m/s on a horizontal section of track , as shown in the figure at “click here”. It rolls around the inside of a vertical circular loop 90.0 cm in diameter and finally leaves the track at a point 20.0 cm below the horizontal section .(a) Find the speed of the ball at the top of the loop . Demonstrate that it will not fall from the track .
(b) Find its speed as it leaves the track .
(c) Suppose that static friction between the ball and track were negligible , so that the ball slid rather instead of rolling . Would its speed then be higher , lower , or same at the top of the loop ?
Physics Rotational Mechanics Level: High School
The top shown has a moment of inertia of 4.00 x 10^-4 kgm^2 and is initially at rest . It is free to rotate about the stationary axis AA’. A string wrapped around a peg along the axis of the top , is pulled in such a manner as to maintain a constant tension of 5.57 N , If the string does not slip while it is unwound from the peg , what is the angular speed of the top after 80.0 cm of string has been pulled off the peg ?
Physics Rotational Mechanics Level: High School
A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M= 10.0 kg . These blocks are allowed to move on a fixed block-wedge of angle theta = 30 degrees as shown at “click here” . The coefficient of kinetic friction is 0.36 for both blocks . Draw a free-body diagrams of both blocks , as well as the pulley . Determine(a) The acceleration of the two blocks.
(b) The tensions in the string on both sides of the pulley.
Physics Rotational Mechanics Level: High School
Many machine employ cams for various purposes , such as opening and closing valves . In this problem , our cam is a circular disc rotating on a shaft that does not pass through the center of the disk . In the manufacture of the cam, a uniform solid cylinder of radius R is first machined . Then an off-center hole of radius R/2 is drilled , parallel to the axis of the cylinder , and centered at a point a distance R/2 from the center of the cylinder . The cam of mass M , is then slipped onto a cylindrical shaft and welded into a place . What is the kinetic energy of the cam when it is rotating with angular speed w(omega) about the axis of the shaft ?
Physics Rotational Mechanics Level: High School
Calculate the moment of inertia of a thin plate, in the shape of a right triangle as shown in the figure at “click here” . Let M represents the mass of the triangle and L the length of the base of the triangle perpendicular to the axis of rotation . Let h represent the height of the triangle and w(omega) the thickness of the plate , much smaller than L or h. Use the integral form of the moment of inertia equation . Let an element of mass consist of a vertical ribbon within the triangle , of width dx , height y, and thickness w . With x representing the location of the ribbon, show that y = hx/L . Show that the density of material is given by p=2M/L wh . Show that the mass of the ribbon is dM = pywdx = 2Mxdx/L^2 . Then calculate the moment of inertia from the integral equation .