respect to the origin at t = 1 sec i D. 10 C. 8 E. 12 Q.20: in the adjacent figure, a very light rope is wrapped around a wheel of radius R = 2 m. The wheel can rotate around an axle that is passing through its center and perpendicular to its surface. A block of mass 14 kg is suspended (üa) from he end of the rope, When the system is reieased from rest it is observed that the -lock descends (i) with constant acceleration of magnitude 5 m/s. he moment of inertia (measured in kg.m) of the wheel relative to the rotation -le is: 9.8 B. 37.2 C. 12.8 24.3 E. 53.8
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![Q.15: The angular position (s yall) of a swinging () rigid body is given by:
0(t) = (--43 + 2t² + 1001 + 5) rad
The magnitude of the angular velocity (in rad/s) of this body at t = 1 sec is:
В. 18
C. 23
D. 92
E.
A. 9.8
Q.16: At t = 0, a wheel (Jae) rotating about a fixed axis at a constant angular acceleration hi
angular speed of 2 rad/s. Two seconds later it has turned through 5 complete revolutions (
The magnitude of the angular acceleration (in rad/s) of this wheel is:
(Hint: one revolution equals 2n rad).
A. 2.65
Q.17: The disc in the adjacent figure has radius R and rotates () with an angular speed w al
axle (J) passing through point o and perpendicular (sc) to the plane of the disc. Let w, a
represent the angular speed, angular acceleration and linear speed,
respectively (al gle). If points A, B, and C lie at the rim (a) of the disc,
then which of the following statements is entirely (S) correct:
A. VA> Va> Vc and wa = Wa = ws
B. VA = Va = Vc and wa> wa> wc
C. an >ag > ac and VA = Vg = Vc
D. WA = Wg = wcand Vc> Vg > VA
[. WA = Wa = we and VA = Va = Vc
Q.18: A rigid body rotates around an axis that passes through the origin and perpendicular to its
surface. A force F= (2i + i -k)N acts on the rigid body at the point (1, -1, 1) m.
The magnitude of the torque (in N.m) due to this force calculated about the origin is:
B. 5.0
C. 13.7
D. 9.8
E.
A. 2.1
B. 4.2
C. 6.0
D. 18
E. 23
Q.19: A 2-kg particle has its position in the XY-plane given by:
F(1) ={(24 + 5)i +(1 - 31 +1)], where t is in seconds andr is in meters. The magnitude of
the angular momentum (measured in kg.m²/s Jof the particle with respect to the origin at t = 1 sec i
A. 2
В. 6
С. 8
D. 10
E. 12
Q.20: in the adjacent figure, a very light rope is wrapped around a wheel of radius
R = 2 m. The wheel can rotate around an axte that is passing through its center
and perpendicular to its surface. A block of mass 14 kg is suspended (ilea) from
-he end of the rope. When the system is reieased from rest it is observed that the
-lock descends () with constant acceleration of magnitude 5 m/s.
he moment of inertia (measured in kg.m) of the wheel relative to the rotation
-ie is:
14 kg
B. 37.2
E. 53.8
9.8
C. 12.8
24.3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0bd804a-f33b-4e5b-b94a-bc9f6cb6691c%2Fea339afd-c559-4545-9e7a-ecf792f581cf%2Fsuyjfey_processed.jpeg&w=3840&q=75)
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