A 1.10 kg solid, uniform disk of radius 0.180 m is released from rest at point A in the figure below, its center of gravity a distance of 1.80 m above the ground. The disk rolls without slipping to the bottom of an incline and back up to pointB where it is launched vertically into the air. The disk then rises to its maximum height hmay at point C.HINTU = 01.80 mhmaxT0.350 m(a) At point B, find the disk's translational speed ve (in m/s).m/s(b) At point B, find the disk's rotational speed w, (in rad/s).rad/s(c) At point C, find the disk's rotational speed w. (in rad/s).rad/s(d) At point C, find the maximum height hay of the disk's center of gravity (in m).m

Solution:- Given m=1.10 kg r=0.180 m. (Solid uniform disk ) h1=1.80 m h2=0.350 m

A 1.10 kg solid, uniform disk of radius 0.180 m is released from rest at point A in the figure below, its center of gravity a distance of 1.80 m above the ground. The disk rolls without slipping to the bottom of an inctine and back up to point B where it is launched vertically into the air. The disk then rises to its maximum height hy at point C. HINT V= 0 1.80 m hmax 0.350 m (a) At point B, find the disk's translational speed va (in m/s). m/s (b) At point B, find the disk's rotational speed wn (in rad/s) rad/s (c) At point C, find the disk's rotational speed w (in rad/s). rad/s (d) ot noint C. find the maximum height h of the disk's center of gravity (in m).

A 1.10 kg solid, uniform disk of radius 0.180 m is released from rest at point A in the figure below, its center of gravity a distance of 1.80 m above the ground. The disk rolls without slipping to the bottom of an inctine and back up to point B where it is launched vertically into the air. The disk then rises to its maximum height hy at point C. HINT V= 0 1.80 m hmax 0.350 m (a) At point B, find the disk's translational speed va (in m/s). m/s (b) At point B, find the disk's rotational speed wn (in rad/s) rad/s (c) At point C, find the disk's rotational speed w (in rad/s). rad/s (d) ot noint C. find the maximum height h of the disk's center of gravity (in m).

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 10P: A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a...

See similar textbooks

Similar questions

A hollow cylinder that is rolling without slipping is given a velocity of 5.0 m/s and rolls up an incline to a vertical height of 1.0 m. If a hollow sphere of the same mass and radius is given the same initial velocity how high vertically does it roll up the incline?
A top has moment of inertia 3.2104kgm2 and radius 4.0 cm from the center of mass to the pivot point. If it spins at 20.0 rev/s and is precessing, how many revolutions does it precess in 10.0 s?
A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M=0.10kg,R=0.10m) rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, what is the angular velocity of the disk then? (d) What is the new kinetic energy of the system? (e) What is the cause of the increase and decrease of kinetic energy?
A baseball catcher extends his arm straight up to catch a fast ball with a speed of 40 m/s. The baseball is 0.145 kg and the catcher’s arm length is 0.5 m and mass 4.0 kg. (a) What is the angular velocity of the arm immediately after catching the ball as measured from the arm socket? (b) What is the torque applied if the catcher stops the rotation of his arm 0.3 s after catching the ball?
A solid cylinder of radius 10.0 cm rolls down an incline with slipping. The angle of the incline is 30 . The coefficient of kinetic friction on the surface is 0.400. What is the angular acceleration of the solid cylinder? What is the linear acceleration?
The precession angular velocity of a gyroscope is 1.0 rad/s. If the mass of the rotating disk is 0.4 kg and its radius is 30 cm, as well as the distance from the center of mass to the pivot, what is the rotation rate in rev/s of the disk?
What three factors affect the torque created by a force relative to a specific pivot point?
The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min. (a) If the blades are 6000 kg each and the rotor assembly has three blades, calculate the angular momentum of the turbine at this rotation rate. (b) What Is the torque require to rotate the blades up to the maximum rotation rate in 5 minutes?
Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis through their centers. Both spheres have the same mass and radius. Which sphere, if either, has the higher rotational kinetic energy? (a) The hollow I sphere, (b) The solid sphere, (c) They have the same kinetic energy.
A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different moments, its angular speed is 2 rad/s, 0. and +2 rad/s. For a point on the rim of the wheel, consider at these moments the magnitude of the tangential component of acceleration and the magnitude of the radial component of acceleration. Rank the following five items from largest to smallest: (a) |at| when = 2 rad/s, (b)|ar| when = 2 rad/s, (c)|ar| when = 0, (d) |at| when = 2 rad/s, and (e) |ar| when = 2 rad/s. If two items are equal, show them as equal in your ranking. If a quantity is equal to zero, show that fact in your ranking.
A uniform rod of length L and mass M is held vertically with one end resting on the floor as shown below. When the rod is released, it rotates around its lower end until it hits the floor. Assuming the lower end of the rod does not slip, what is the linear velocity of the upper end when is hits the floor?
Check Your Understanding What is the moment of inertia of a cylinder of radius R and mass m about an axis through a point on the surface, as shown below? A uniform thin disk about an axis through the center Integrating to find the moment of inertia of a two-dimensional object is a little bit trickier, but one shape is commonly done at this level of study—a uniform thin disk about an axis through its center (Figure 10.27). Figure 10.27 Calculating the moment of inertia for a thin disk about an axis through its center.