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

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genius_generous answered 1 year ago

A thin uniform disk of radius r and mass m is spinning about its center at...

A thin uniform disk of radius r and mass m is spinning about its center at angular speed ω0. The disk is placed flat on a horizontal surface. The coefficient of kinetic friction between the disk and the surface is μ and constant for the entire area of contact. a) Find the frictional torque on the disk. (Hint: Divide the disk into many concentric rings.) b) How long will it take the disk to come to rest?

A thin, uniform disk with mass M and radius R is pivoted about a fixed point...

A thin, uniform disk with mass M and radius R is pivoted about a fixed point a distance x from the center of mass. The disk rotates around the fixed point, with the axis of rotation perpendicular to the plane of the disk. What is the period as a function of x, M, R, and acceleration due to gravity (g), and what is the distance x that gives the smallest period?

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 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 =...

A uniform disk with mass m = 9.44 kg and radius R = 1.32 m lies...

A uniform disk with mass m = 9.44 kg and radius R = 1.32 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 318 N at the edge of the disk on the +x-axis, 2) a force 318 N at the edge of the disk on the –y-axis, and 3) a force 318 N acts at the edge of the disk at an angle θ =...

1. A uniform disk of mass M = 5.00 kg and radius r = 24.0 cm...

1. A uniform disk of mass M = 5.00 kg and radius r = 24.0 cm is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1.50 N · m. (a) What is the time required for the disk to reach an angular speed of 8.50 ✕ 102 rpm? (b) What is the number of revolutions through which the disk spins before reaching this angular speed? 2. A...

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...

Consider a uniform density sphere of mass M and radius R in hydrostatic equilibrium with zero...

Consider a uniform density sphere of mass M and radius R in hydrostatic equilibrium with zero surface pressure. Derive expressions for the pressure P(r) and the gravitational potential phi(r) in terms of r, M, R, G and constants.

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?

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