A uniform rigid disk of radius r and mass m rolls without slipping on a smooth horizontal surface. A constant force of magnitude P is applied to the rim of the disk at distance r above the horizontal surface and in the direction of motion. r,m,P are known.

what is the angular acceleration in terms of known quantities, and what force P will cause the disk to begin slipping if the coefficient of static friction is u between disk and horizontal surface? what distance d will the disk's center of mass have traveled when it reaches a speed v?

Solution Preview

A uniform rigid disk of radius r and mass m rolls without slipping on a smooth horizontal surface. A constant force of magnitude P is applied to the rim of the disk at distance r above the horizontal surface and in the direction of motion. r,m,P are known.

What is the angular acceleration in terms of known quantities, and what force P will cause the disk to begin slipping if the coefficient of static friction is u between disk and horizontal surface? what distance d will the disk's center of mass have traveled when it reaches a speed v?

Answer:

First, a quick sketch to give us an idea of what is happening:

The torque on the disk is a little strange, but we'll get to that. The rolling motion occurs because the ...

Solution Summary

The mechanics of angular acceleration quantities are given. The static friction between disk and horizontal surfaces are analyzed.

Question: Bar BDE is attached to two links AB and CD. Knowing that at the instant shown link AB rotates with a constant angular velocity of 3 rad/s clockwise, determine the acceleration (a) of point D, (b) of point E.
Please refer to attachment to see a diagram of this scenario.

A disk of mass M and radius R unwinds from a tape wrapped around it. The tape passes over a frictionless pulley, and a mass m is suspended from the other end. Assume that the disk drops vertically.
a) Relate the accelerations of m and the disk, a and A, respectively to the angular acceration of the disk.
Ans clue- If A we

(Please see the attachment for questions, complete with diagrams/figures)
2. If the 10-kg ball has a velocity of 3 m/s when it is at the position A, along the vertical path, determine the tension in the cord at this position and the magnitude of acceleration of the ball at this position.
3. The 2-Mg car is being towed by

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s.
a) Before slowing, what is the speed of a child on the rim? (in m/s)
b) How many revolutions does the merry-go-round make as it stops?

Question: The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angularacceleration as the blades slow down? The initial rotation is in the positive direction.

A certain CD has a playing time of 78 minutes. When the music starts, the CD is rotating at an angular speed of 4.8 * 10^2 revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.1 * 10^2 rpm. Find the magnitude of the average angularacceleration of the CD. Express your answer in rad/s2.

Q: "The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angularacceleration as the blades slow down? The initial rotation is in the positive direction."
The OTA's solution is attached. We both got an answer of 208 rad/s^2.

Please see the attached file.
5/139. The sliding collar moves up and down the shaft, causing an oscillation of crank OB. If the velocity of A is not changing as it passes the null position where AB is horizontal and OB is vertical, determine the angularacceleration of OB in that position.

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angularacceleration of 0.745 rad/s^2. The child is standing 4.65m from the center of the merry-go-round. What angle does the acceleration of the child make with the tangential direction?