MSD210 Dynamics 2022
Department of Mechanical and Aeronautical Engineering
University of Pretoria
Homework Assignment 2: Rigid body rotation
For: 1 or 2 March 2022
• Homeworks are assigned on a Thursday, based on the material from the week’s
lectures, and should be completed by your tutorial session on the following
Tuesday or Wednesday.
• The purpose of the homework is to give you an opportunity to practice and
apply the skills and concepts covered in class. To help you as you study, the
key concepts covered in this week’s homework are identified.
• Please attempt to complete the homework before the tutorial session, this will
allow you to take advantage of the tutorial sessions to get help from the lecturer
for aspects of the work that you do not understand.
• Homework will not be submitted for marking. You are welcome to collaborate with your classmates, although you should ensure once you complete the
homework that you can do all the work yourself.
• Practice writing neat and coherent solutions.
Key concepts this week
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• Calculating the position vector r
• Relationship between velocity and angular velocity
• Relationship between acceleration and angular acceleration
• Difference between normal acceleration and tangential acceleration
• When to use the scalar form instead of the vector form
Problems / Probleme: Do problems 5/4, 5/11 and 5/16 from Meriam, Kraige
& Bolton edition 9, as well as problems 5/2, 5/7 and 5/16 from Meriam, Kraige &
Bolton edition 8. The problems are all given in this homework document.
1
Problem 5/2 from MKB8 (not in MKB9)
The circular section rotates about a fixed axis through point O with angular velocity
ω = 2 rad/s and angular acceleration α = 4 rad/s2 with directions as indicated in
the figure. Determine the instantaneous velocity and acceleration of point A.
Problem 5/4 (5/3 from MKB8)
The angular velocity of a gear is controlled according to ω = 12 − 3t2 where ω, in
rad/s, is positive in the clockwise sense and where t is the time in seconds. Find the
net angular displacement ∆θ from the time t = 0 to t = 3 s. Also find the total
number of revolutions N through which the gear turns during the 3 seconds.
2
Problem 5/7 from MKB8 (not in MKB9)
The flywheel has a diameter of 600 mm and rotates with increasing speed about its
z-axis shaft. When point P on the rim crosses the y-axis with θ = 90◦ , it has an
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acceleration given by a = −1.8 i − 4.8 j m/s2 . For this instant, determine the angular
velocity ω and the angular acceleration α of the flywheel.
Problem 5/11 (5/15 from MKB8)
In order to test an intentionally weak adhesive, the bottom of the small 0.3 kg block is
coated with adhesive, and then the block is pressed onto the turntable with a known
force. The turntable starts from rest at time t = 0 and uniformly accelerates with
α = 2 rad/s2 . If the adhesive fails at exactly t = 3s, determine the ultimate shear
force which the adhesive supports. (Hint: Remember, F = ma!) What is the angular
displacement of the turntable at the time of failure?
3
Problem 5/16 from MKB8 (not in MKB9)
The two attached pulleys are driven by the belt with increasing speed. When the
belt reaches a speed v = 0.6 m/s, the total acceleration of point P is 8m/s2 . For this
instant determine the angular acceleration α of the pulleys and the acceleration of
point B on the belt.
Problem 5/16 (5/20 from MKB8)
Develop general expressions for the instantaneous velocity and acceleration of point
A of the square plate, which rotates about a fixed axis through point O. Take all
variables to be positive. Then evaluate your expressions for θ = 30◦ , b = 0.2 m,
ω = 1.4 rad/s and α = 2.5 rad/s2 .
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