School of Mechatronic Systems Engineering
MSE 222 - Homework 1 (Solutions)
Problem 1: The mass of the homogeneous thin plate is
20-kg. Determine its moment of inertia about axis 𝑥.
Problem 2: The object consists of the 2-kg slender bar 𝐴𝐵𝐶
welded to the 3-kg slender bar 𝐵𝐷𝐸. The 𝑦 axis is vertical. At
the instant shown, the object has a counter-clockwise angular
velocity of 5 rad/s. Determine the components of the force
exerted on it by the pin support.
Problem 3: A thin ring and a homogeneous circular disk, each
of mass 𝑚 and radius 𝑅, are released from rest on an inclined
surface. Determine the ration 𝑣
/𝑣
of the velocities of the
their centers when they have rolled a distance 𝐷.
Problem 4: The 100-kg cylindrical disk is at rest when the force 𝐹
is applied to a cord wrapped around it. The static and kinetic
coefficients of friction between the disk and the surface is 0.2.
Determine the angular acceleration of the disk if
a) 𝐹
b) 𝐹
500 N
1000 N
Page 1 of 2
School of Mechatronic Systems Engineering
Problem 5: As a result of the constant couple 𝑀 applied to the 1-kg
disk, the angular acceleration of the 0.4-kg slender bar is zero.
Determine 𝑀 and the angular acceleration of the rolling disk.
Problem 6: The slender bars each weigh 17.8 N and are 254
mm long. The homogenous plate weighs 44.5 N. If the system
is released from rest in the position shown, what is the angular
acceleration of the bars at that instant?
Problem 7: The 18-kg ladder is released from rest in the position shown.
Determine its angular acceleration at the instant of release. Neglect
friction.
Page 2 of 2