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A horizontal platform in a shape of a disk rotates on a frictionless bearing ab…

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Wize University Physics Textbook (Master) > Angular / Rotational Motion

Conservation of Angular Momentum

3 Activities

Wize University Physics Textbook (Master) > Angular / Rotational Motion

Moment of Inertia

5 Activities

A horizontal platform in a shape of a disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 200 kg and radius of 3.0 meters. A student with mass 80 kg, walks from the edge towards the center of the platform.
a) Find the moment of inertia of the disk.
b) If the angular speed of the disk is 2 rad/s, when the student moves another meter towards the center, find their angular speed.
More Conservation of Angular Momentum Questions:
angular momentum and conservation of angular momentum
A satellite is rotating once per minute. It has a moment of inertia of 10,000kg⋅m2. Erin, an astronaut, extends the satellite's solar panels, increasing its moment of inertia to 30,000kg⋅m2. How quickly is the satellite now rotating?
Friction turntable
Practice: Friction Turntable
Three blocks are placed on a spinning turntable at increasing distances away from the center of the turntable. Recall that the tangential velocity increases towards the edge of the turntable. The coefficient of static friction for all three blocks is the same, and they have the same mass. As the velocity of the turntable increases, which block slips first? Why?
A kid with mass m and velocity v runs toward a playground merry-go-round, which is initially at rest, and jumps on at its edge. The kid and the merry-go-round (mass M, radius R, and I = cMR2) then spin together.
We use the expression I = cMR2 because the merry-go-round is a complicated shape and we can't call it just a cylinder or a disk; c is some number between 0 and 1.
a) If the kid's initial velocity is tangent to the circular merry-go-round, what is the angular velocity after jumping on? Write your answer in terms of the other variables (mass, radius, C, and the tangential velocity). Then input your answer using m=30kg;M=150kg;C=0.55;R=2.3m;v=2.5m/sm=30kg; M = 150 kg; C = 0.55; R = 2.3 m; v = 2.5 m/s.
A professional diver bends to reduce her moment of inertia by a factor of 1.8 before diving into a pool. What happens to her angular velocity, compared to if she had not bent before diving?
A uniform, spherical cloud of gas and dust from Orion has mass 2.0×1030 kg2.0\times10^{30}~\rm kg, has a radius of 1.0×1013 m1.0\times10^{13}~\rm m, and is rotating with a period of 1.4×1061.4\times10^6 years. The cloud collapses to form a star 7.0×108 m7.0\times10^8~\rm min radius. Find the star's period of rotation. Enter your result in days. (Moment of inertia for a solid sphere about an axis is 25MR2\frac25MR^2).
(In case you did not know: like all stars, the sun does rotate! Our sun's rotation period is 24 days.)
Ballistic pendulum and momentum
A ballistic pendulum is used to measure the speed of a bullet. It consists of a wooden block of mass M = 10kg suspended from a vertical string. A bullet of mass m = 100g strikes and embeds itself in the block and the block swings upward through a vertical distance of 0.10m. What was the bullet's speed? Enter your answer in m/s.
Object strikes a rod
An object of mass m and speed v0 strikes the bottom of a rigid uniform rod of length l and mass M that is hanging by a frictionless pivot in a wall. The pivot is through the center of mass of the rod, and is fastened to a wall, so that the rod can rotate about its center. Immediately after striking the rod, the object continues forward with half its initial speed.
a) Find the angular speed immediately after the collision
b) For what value of v0 will the rod just reach a horizontal position (before falling back down again)?
Spinning with a weight
You're sitting on a rotating stool, initially rotating at 3.0 radians per second. You're holding a 5.0 kg dumbbell very close to you, 0.05 meters away from your center of rotation. You then extend your arms 1.0 meters away from you with the dumbbell. The moment of inertia of you and the stool is 4.0 kg m2. Neglect the mass of your arms and any rotational friction in the seat.
a) What is your new angular velocity?
b) How would this question be different if you held a 2.5 kg dumbbell in each hand, instead of a single 5.0 kg weight, and extended them the same length?
Friction turntable
Three blocks are placed on a spinning turntable at increasing distances away from the center of the turntable. Recall that the tangential velocity increases towards the edge of the turntable. The coefficient of static friction for all three blocks is the same, and they have the same mass. As the velocity of the turntable increases, which block slips first? Why?
A rod is 3m long and rotates at ωo=5 rad/s.\omega_o=5~\rm rad/s.It is heated and expands to 3.2m. What is its new ω?\omega?
A uniform, spherical cloud of gas and dust from Orion has mass 2.0×1030 kg2.0\times10^{30}~\rm kg, has radius 1.0×1013 m1.0\times10^{13}~\rm m, and is rotating with a period of 1.4×1061.4\times10^6, years. The cloud collapses to form a star 70×108 m70\times10^8~\rm min radius. Find the star's rotation period.
A professional diver bends to reduce her moment of inertia by 1.8 times the initial moment of inertia and then dives into a pool. What happens to her angular velocity? Does it increase or decrease and by how much?
A kid with mass m and velocity v runs toward a playground merry-go-round, which is initially at rest, and jumps on at its edge. The kid and the merry-go-round (mass M, radius R, and I = cMR2) then spin together with a constant angular velocity ωf.
If kid's initial velocity is tangent to the circular merry-go-round, what is ωf?
What is the energy loss?
A horizontal platform in a shape of a disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 200 kg and radius of 3m. A student with mass 80 kg, walks from the edge towards the center of the platform.
a) Find the moment of inertia of the disk
b) If the angular speed of the disk is 2 rad/s, when the student gets to 1 m towards the center, find the angular speed
An object of mass m and speed v0 strikes a rigid uniform rod of length l and mass M that is hanging by a frictionless pivot from the ceiling. Immediately after striking the rod, the object continues forward with half its initial speed.
a) Find the angular speed immediately after the collision
b) For what value of v0 will the rod just touch the ceiling?
A ladybug is on a rotating disk of radius R, moving steadily and radially toward the center of the disk as the disk rotates with constant angular velocity ω\omega. Which statement(s) is correct about the motion of the lady bug?
a) Its acceleration vector is always toward the center.
b) Its velocity vector has only a tangential component.
angular momentum and conservation of angular momentum
A satellite is rotating once per minute. It has a moment of inertia of 10,000kg⋅m2. Erin, an astronaut, extends the satellite's solar panels, increasing its moment of inertia to 30,000kg⋅m2. How quickly is the satellite now rotating?
More Moment of Inertia Questions:
Moment of inertia is same as linear inertia
Instead of mass (used in translational motion), what do we use in the equation for rotational kinetic energy instead?
A mass-less string is wrapped several times around a Cylinder . If the free end of the string is held in place and the Cylinder is released form rest, the string unwinds and the Cylinder descends. What is the acceleration of the Cylinder ?
A thin uniform rod (length=1m, mass = 5kg) is pivoted about a horizontal, frictionless pin through one end of the rod. The rod is released when it makes an angle of 60°60\degree above the horizontal. What is the angular acceleration of the rod at the instant it is released? (pick the closest answer)
Two thin Hoops each of mass M and radius of R are joined together as shown in the figure. What is the moment of inertia for rotations in the plane of the page about pint O?
A 10 kg mass is hanging from a rope wrapped around a pulley. The falling mass causes the pulley to rotate. The mass of the pulley is 2 kg. What is the acceleration of the falling mass, and what is the tension of the rope?
Robin Hood and Marian decide to build a snowmen at the edge of a cliff.  The snowman consists of three spheres with radii 90 cm, 60 cm and 30 cm, and the density of snow is 300kg/m3300kg/m^3.  Little John is a jerk and pushes the snowman over the cliff.  The snowman begins to rotate around its center of mass as it falls.  What is the moment of inertia of the snowman as it’s falling? (For a solid sphere, ICM=25MR2 , and  V=43πR3I_{CM}=\frac{2}{5}MR^2\ ,\ and\ \ V=\frac{4}{3}\pi R^3, )
A potter's wheel of mass 7.00 kg and radius 0.650 m spins about its central axis. A 2.10 kg lump of clay is dropped onto the wheel at a distance 0.410 m from the axis. Calculate the final rotational inertia of the system.
Rotational inertia depends on the force of gravity
moment of interia
What does the moment of inertia describe?
The moment of inertia of a body depends on