A solid disk of mass M and radius R is rotating on the vertical axle with...

A solid disk of mass M and radius R is rotating on the vertical axle with angular speed w. Another disk of mass M/2 and radius R, initally not rotating, falls coaxially on the disk and sticks. The rotational velocity of this system after collision is:

w/2

2w/3

3w/2

Solutions

Expert Solution

Mass of the first disk = M

Radius of the first disk = R

Moment of inertia of the first disk = I₁

I₁ = MR²/2

Initial angular velocity of the first disk = ₁ =

Mass of the second disk = M/2

Radius of the second disk = R

Moment of inertia of the second disk = I₂

I₂ = (M/2)R²/2

I₂ = MR²/4

Initial angular velocity of the second disk = ₂ = 0 rad/s

Final angular velocity of both the disk = ₃

By conservation of angular momentum,

I₁₁ + I₂₂ = (I₁ + I₂)₃

(MR²/2)() + (MR²/4)(0) = (MR²/2 + MR²/4)₃

₃ = 2/3

Rotational velocity of the system after the collision = 2/3

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A solid disk of mass m1 = 9.3 kg and radius R = 0.22 m is...

A solid disk of mass m1 = 9.3 kg and radius R = 0.22 m is rotating with a constant angular velocity of ω = 31 rad/s. A thin rectangular rod with mass m2 = 3.9 kg and length L = 2R = 0.44 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? 2) What...

A solid disk of mass m1 = 9.9 kg and radius R = 0.2 m is...

A solid disk of mass m1 = 9.9 kg and radius R = 0.2 m is rotating with a constant angular velocity of ω = 35 rad/s. A thin rectangular rod with mass m2 = 3.1 kg and length L = 2R = 0.4 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? 2) What...

A uniform disk of mass M and radius R is initially rotating freely about its central...

A uniform disk of mass M and radius R is initially rotating freely about its central axis with an angular speed of w, and a piece of clay of mass m is thrown toward the rim of the disk with a velocity v, tangent to the rim of the disk as shown. The clay sticks to the rim of the disk, and the disk stops rotating. What is the magnitude of the total angular momentum of the clay-disk system before...

A disk of radius a and mass m is suspended at its centre by a vertical...

A disk of radius a and mass m is suspended at its centre by a vertical torsion wire which exerts a couple -cθ on the disk when it is twisted through an angle θ from its equilibrium position. Show that oscillations of the disk are simple harmonic, and obtain an expression for the period. A wire ring of mass m and radius a/2 is dropped concentrically onto the disk and sticks to it. Calculate the changes to (a) the period...

Consider a thin uniform disk of mass M and radius R. A mass m is located...

Consider a thin uniform disk of mass M and radius R. A mass m is located along the axis of the disk at a distance z from the center of the disk. The gravitational force on the mass m (in terms of m, M, R, G, and z) is

A certain wheel is a uniform disk of radius R = 0.5 m and mass M...

A certain wheel is a uniform disk of radius R = 0.5 m and mass M = 10.0 kg. A constant force of Fapp = 15.0 N is applied to the center of mass of the wheel in the positive x-direction. The wheel rolls along the ground without slipping. (a) Compute the rotational inertia of the wheel about its center of mass. (b) Compute the magnitude and direction of the friction force acting on the wheel from the ground. (c)...

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at...

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ω = 31 rad/s. 1.What is the angular acceleration of the disk? 2. What is the angular displacement over the 17.2 s? 3. What is the moment of inertia of the disk? 4. What is the change in rotational energy of the disk?

Find the moment of inertia of a circular disk of radius R and mass M that...

Find the moment of inertia of a circular disk of radius R and mass M that rotates on an axis passing through its center. [Answer: ½ MR2] Step 1: Pictorial representation: Sketch a neat picture to represent the situation. Step 2: Physical representation: 1) Cut the disk into many small rings as it has the circular symmetry. 2) Set up your coordinate system and choose its origin at the pivot point (or the axle location) for convenience. Then choose a...

A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies...

A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 313 N at the edge of the disk on the +x-axis, 2) a force 313 N at the edge of the disk on the –y-axis, and 3) a force 313 N acts at the edge of the disk at an angle θ =...

A uniform disk with mass m = 9.28 kg and radius R = 1.42 m lies...

A uniform disk with mass m = 9.28 kg and radius R = 1.42 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 345 N at the edge of the disk on the +x-axis, 2) a force 345 N at the edge of the disk on the –y-axis, and 3) a force 345 N acts at the edge of the disk at an angle θ =...

Subjects