Two point masses,m,= 1 kg and m, =2 kg, are suspended by a massles length (= 1 m. The rod is pivoted a distance d = 0.25 m from the left er (a) What is the moment of inertia of the system about the pivot point? [- rotational inertia of a single point mass is I ma = mr, where r is the from the mass to the axis of rotation. To find the total rotational iner system, you simply add the individual rotational inertias. This is jus find total mass of a system by adding the individual masses.] b) Draw a free body force diagram for the rod. Remember that it is now draw the forces on the body where they actually act. c) Convince yourself (and the others in your group) that the torque abo point due to gravity acting on m, is out of the page, while that due to acting on m, is into the nage Find umoni
Two point masses,m,= 1 kg and m, =2 kg, are suspended by a massles length (= 1 m. The rod is pivoted a distance d = 0.25 m from the left er (a) What is the moment of inertia of the system about the pivot point? [- rotational inertia of a single point mass is I ma = mr, where r is the from the mass to the axis of rotation. To find the total rotational iner system, you simply add the individual rotational inertias. This is jus find total mass of a system by adding the individual masses.] b) Draw a free body force diagram for the rod. Remember that it is now draw the forces on the body where they actually act. c) Convince yourself (and the others in your group) that the torque abo point due to gravity acting on m, is out of the page, while that due to acting on m, is into the nage Find umoni
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
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Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
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please do question 2 only ... question 1 is for reference only
![1. Two point masses, m, = 1 kg and m, = 2 kg, are suspended by a massless rod of total
length (= 1 m. The rod is pivoted a distance d= 0.25 m from the left end as shown.
(a) What is the moment of inertia of the system about the pivot point? [Hint: the
rotational inertia of a single point mass is I mass = mr, where r is the distance
from the mass to the axis of rotation. To find the total rotational inertia of a
system, you simply add the individual rotational inertias. This is just as you would
find total mass of a system by adding the individual masses.]
(b) Draw a free body force diagram for the rod. Remember that it is now important to
draw the forces on the body where they actually act.
(c) Convince yourself (and the others in your group) that the torque about the pivot
point due to gravity acting on m, is out of the page, while that due to gravity
acting on m, is into the page. Find numerically the torque due to each, taking g =
9.8 m/s.
(d) Find the net torque about the pivot point at the instant shown.
(e) Find the angular acceleration about the pivot point at the instant shown.
(H The rod is released from rest from the position shown. Through what angle does
the rod rotate in the next 0.001 s? Assume that the angular acceleration is constant
through this short time interval.
[Ans: (a) I, = 1.19 kg m²; (d) Et, = 12.25 N m, in which direction?; (e) ap = 10.3 rad/s², in which
direction?; (f) 5.2 x 1oʻrad]
m1
m2
Problem 1
Problem 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd262417-6fb5-41dd-a016-065cc7d50841%2F5a194485-57e4-494a-81f8-da8a62cbec47%2F1n28oh_processed.png&w=3840&q=75)
Transcribed Image Text:1. Two point masses, m, = 1 kg and m, = 2 kg, are suspended by a massless rod of total
length (= 1 m. The rod is pivoted a distance d= 0.25 m from the left end as shown.
(a) What is the moment of inertia of the system about the pivot point? [Hint: the
rotational inertia of a single point mass is I mass = mr, where r is the distance
from the mass to the axis of rotation. To find the total rotational inertia of a
system, you simply add the individual rotational inertias. This is just as you would
find total mass of a system by adding the individual masses.]
(b) Draw a free body force diagram for the rod. Remember that it is now important to
draw the forces on the body where they actually act.
(c) Convince yourself (and the others in your group) that the torque about the pivot
point due to gravity acting on m, is out of the page, while that due to gravity
acting on m, is into the page. Find numerically the torque due to each, taking g =
9.8 m/s.
(d) Find the net torque about the pivot point at the instant shown.
(e) Find the angular acceleration about the pivot point at the instant shown.
(H The rod is released from rest from the position shown. Through what angle does
the rod rotate in the next 0.001 s? Assume that the angular acceleration is constant
through this short time interval.
[Ans: (a) I, = 1.19 kg m²; (d) Et, = 12.25 N m, in which direction?; (e) ap = 10.3 rad/s², in which
direction?; (f) 5.2 x 1oʻrad]
m1
m2
Problem 1
Problem 2
![2. At some later time the rod in Problem 1 has rotated through an angle = 30° as shown.
(a) Draw a free body force diagram for the rod in this new position.
(b) Calculate the net torque about the pivot point at the instant shown.
(c) Find the angular acceleration about P at the instant shown.
[Ans: (b) Er,= 10.6 N m, in which direction?; (c) a, = 8.9 rad/s² in which direction?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd262417-6fb5-41dd-a016-065cc7d50841%2F5a194485-57e4-494a-81f8-da8a62cbec47%2Fpoomvhe_processed.png&w=3840&q=75)
Transcribed Image Text:2. At some later time the rod in Problem 1 has rotated through an angle = 30° as shown.
(a) Draw a free body force diagram for the rod in this new position.
(b) Calculate the net torque about the pivot point at the instant shown.
(c) Find the angular acceleration about P at the instant shown.
[Ans: (b) Er,= 10.6 N m, in which direction?; (c) a, = 8.9 rad/s² in which direction?]
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