Problem 3: A solid object made of two cylinders of uniform density is initially at rest at time t = 0. A constant couple of M = (0,0,30)N m is applied to the object, causing it to rotate about the z-axis (which goes through the center of the cylinders). The 0.5-m cylinder has a mass of 10 kg. The 1-m cylinder has a mass of 25 kg. A perspective and plan view of the composite shape are shown in Figure 3. Note that the moment of inertia of a cylinder about its center of mass is mR² where m is the mass and R is the radius of the cylinder. M = (0,0,30) N-m Figure 3: Perspective view (left) and plan view (right). 0.5 m M-(0,0,30) N-m 1 m Given this information, answer the questions below: i) ii) iii) What is the moment of inertia of the composite object about the z-axis? Hint: if we know the moment of inertia of each cylinder about the z-axis, then we can just add them together. What is the angular acceleration of the 0.5m-cylinder? What about the 1m-cylinder? At time t = 5 sec, what is the angular velocity of the 0.5m-cylinder? What about the 1m-cylinder? At time t = 5 sec, what is the magnitude of the acceleration of point A? point B? iv) v) At time t = 5 sec, what is the speed of point A? point B? x
Problem 3: A solid object made of two cylinders of uniform density is initially at rest at time t = 0. A constant couple of M = (0,0,30)N m is applied to the object, causing it to rotate about the z-axis (which goes through the center of the cylinders). The 0.5-m cylinder has a mass of 10 kg. The 1-m cylinder has a mass of 25 kg. A perspective and plan view of the composite shape are shown in Figure 3. Note that the moment of inertia of a cylinder about its center of mass is mR² where m is the mass and R is the radius of the cylinder. M = (0,0,30) N-m Figure 3: Perspective view (left) and plan view (right). 0.5 m M-(0,0,30) N-m 1 m Given this information, answer the questions below: i) ii) iii) What is the moment of inertia of the composite object about the z-axis? Hint: if we know the moment of inertia of each cylinder about the z-axis, then we can just add them together. What is the angular acceleration of the 0.5m-cylinder? What about the 1m-cylinder? At time t = 5 sec, what is the angular velocity of the 0.5m-cylinder? What about the 1m-cylinder? At time t = 5 sec, what is the magnitude of the acceleration of point A? point B? iv) v) At time t = 5 sec, what is the speed of point A? point B? x
Related questions
Question
Please show all steps. Use a format of "v_A/B" to represent velocity of A with respect to B, or something of that manner if needed.
Transcribed Image Text:Problem 3: A solid object made of two cylinders of uniform density is initially at rest at time
t = 0. A constant couple of M = (0,0,30)N m is applied to the object, causing it to rotate
about the z-axis (which goes through the center of the cylinders). The 0.5-m cylinder has a mass
of 10 kg. The 1-m cylinder has a mass of 25 kg. A perspective and plan view of the composite
shape are shown in Figure 3. Note that the moment of inertia of a cylinder about its center of
mass is mR² where m is the mass and R is the radius of the cylinder.
M = (0,0,30) N-m
Figure 3: Perspective view (left) and plan view (right).
0.5 m
M-(0,0,30) N-m
1 m
Given this information, answer the questions below:
i)
ii)
iii)
What is the moment of inertia of the composite object about the z-axis? Hint: if we
know the moment of inertia of each cylinder about the z-axis, then we can just add
them together.
What is the angular acceleration of the 0.5m-cylinder? What about the 1m-cylinder?
At time t = 5 sec, what is the angular velocity of the 0.5m-cylinder? What about the
1m-cylinder?
At time t = 5 sec, what is the magnitude of the acceleration of point A? point B?
iv)
v)
At time t = 5 sec, what is the speed of point A? point B?
x
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
