Purchase Solution

Angular Velocity: Slender Bar, Stepped Disk and Slender Rods

Not what you're looking for?

Ask Custom Question

Please see the attachment for proper formatting and diagrams.

1. The slender bar with a mass of 4 kg is released from rest at an angle of 35 degrees. What is the angular velocity of the bar when it is vertical?

a. 0.667 rad/s

b. 1.06 rad/s

c. 0.888 rad/s

d. 1.74 rad/s

e. 2.31 rad/s

2. The stepped disk weighs 50 lb and its mass moment of inertia about its center is I = 0.4 slug-ft2. If it is released from rest, determine its angular velocity when it falls 3 ft. The rope does not stretch.

a. 22.9 rad/s

b. 10.2 rad/s

c. 8.20 rad/s

d. 32.2 rad/s

e. 15.7 rad/s

3. An assembly consists of two 15-lb slender rods and a 20-lb disk. The spring is unstretched when θ = 45º and the assembly is released from rest at this position. The disk rolls without slipping. Determine the angular velocity of rod AB at the instant θ = 0.

a. 3.89 rad/s

b. 3.65 rad/s

c. 3.12 rad/s

d. 2.69 rad/s

e. 4.28 rad/s

Attachments
Purchase this Solution
Solution Summary

The answers are given step-by-step with some short explanation.

Solution Preview

1.) mass of the rod m = 4 kg
length of the rod l = 2 m
the distance of the pivoted point from the center of the rod r = 0.5 m

Because initial angle of the rod with the vertical, theta = 35 deg
Finally, when the rod is vertical, angle = 0

Hence, loss in potential energy (U) = gain of rotational K.E.,
U = m*g*r*(1 - cos(theta)) = K = (1/2)*I*w^2
NOTE: potential energy is calculated due to change in position of the center of gravity of the rod = r - r*cos(theta)

moment of inertia of the rod about the pivoted point I = m*l^2/12 + m*r^2 = (4*2^2/12) + 4*0.5^2 = 2.33 kg.m^2
angular velocity w = ?
=> w = sqrt(2*m*g*r*(1 - cos(theta)/I)
=> w = sqrt(2*4*9.8*0.5*(1 - cos(35))/2.33) = 1.74 rad/s --Answer (d)

2.) mass of the disc, m = 50 lb
mass moment of inertia about its center, I = 0.4 slug.ft^2 = ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution
Free BrainMass Quizzes
Air Pollution Control - Environmental Science

Working principle of ESP

Architectural History

This quiz is intended to test the basics of History of Architecture- foundation for all architectural courses.

View More Free Quizzes
Related BrainMass Solutions

  • Rotational Motion

    The assembly consists of two 15-lb slender rods and a 20-lb disk. If the spring is unstretched when  = 45° and the assembly is released from rest at this position, determine the angular velocity of rod AB at the instant  = 0°.

  • Mass of Inertia and Angular Acceleration

    37788 Mass of Inertia and Angular Acceleration 1. Two slender rods are welded together at right angles and released from rest as shown. The two welded bars rotate freely around point C. Each bar is 10 lbs and is 1.5 ft long.

  • Slender Bar Angular Acceleration

    46131 SLENDER BAR ANGULAR ACCELERATION The two 10-Kg slender bars (10-m long each) are released from rest in the position shown. Assuming the floor to be smooth, determine the angular acceleration of the bar AB, right after release.

  • Dynamics Problem - Torque and Angular Acceleration

    35549 Dynamics Problem - Torque and Angular Acceleration A slender rod of mass Mr has a disk of mass Mo fastened to it at its end. It is pinned at 0 - a "frictionless" pin.

  • Pendulum Problem of Uniform Plate

    46130 PENDULUM A pendulum consists of a uniform 10-lb plate and a 3-lb slender rod, the whole system swinging around a pin at 0 as shown. At the instant shown (theta = 30) the pendulum has a counterlockwise angular velocity of 5 rad/s.

  • Conservation of Angular Momentum: Suspended Rod

    the ball be v1 and the angular velocity of the rod be w.

  • Mechanics

    At the instant shown, wheel A rotates with angular velocity and angular acceleration shown in the figure.

  • Angular acceleration of the rod

    108770 Angular acceleration of the rod In problem 16.72(a), if the uniform slender rod weighs 15 lb, and the horizontal force P is 12 lb, the angular acceleration of the rod is: a. 44.2 rad/s^2 b. 82.8 rad/s^2 c. 55.2 rad/s^2 d. 35.2 rad/s^2

  • Power transmission velocity

    Let denote OA and BC the angular velocities of rods OA and BC.

View More Related Solutions