(e) 40 rad s 6. During a pirouette a figure skater reduces her moment of inertia from I = 1.24 kg m2 to I2 = 0.25 kg m2 by pulling in her arms. If she rotates with an angular speed of 0.5 rad s-1, before pulling in her arms, what is her final angular speed when she %3D Wi %3D finished the process? (a) 2.48 rad s-2 (b) 0.10 rad s-2 (c) 0.40 rad s-2 (d) 9.92 rad s-2 (e) 0.50 rad s-2 of the same mass and radius roll down an incline,
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.
![1. Determine the moment of inertia I of the Earth on its path around the Sun. Use the
following values:
Mass of the Earth: Mp = 6· 1024 kg
Radius of the Earth's orbit around the Sun: RES = 150 · 106 km
(a) I = 1.35 · 1041 kg m²
(b) I= 5.4 · 1046 kg · m2
(c) I= 6.75 1046 kg · m²
(d) I = 1.35 · 1047 kg · m²
2. Consider problem 1 above. How would the value you found for I change if the Earth's
year were only half as long (i.e. 182.5 days instead of 365 days)?
(a) The value of I would double.
(b) The value of I would be half.
(c) The value of I would not change.
(d) The value of I would quadruple.
(e) The value of I would be one quarter.
3. Consider problem 1 above. How would the value you found for I change if the radius
of the Earth's path around the Sun would be only half as large (i.e. 75 · 106 km
instead of 150 · 106 km)?
94](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95d9a246-e90c-41bd-9705-9a4f0fbd3c96%2F3a290bb8-0721-4816-8f04-cddf41e4978c%2Fl8drurv_processed.jpeg&w=3840&q=75)
![M-8: Rotational Motion
(a) The value of I would double.
(b) The value of I would be half.
(c) The value of I would not change.
(d) The value of I would quadruple.
(e) The value of I would be one quarter.
4. Consider the sketch of the setup for this experiment above. Assume that the tension
in the string running over the pulley is T = 10N and the radius of the pulley is
R = 10 cm. The torque acting on the pulley is
(a) 100 N m
(b) 10N m
(c) 1Nm
(d) 0.1 N m
(e) 0.01 N m
5. Consider problem 4 above. Assuming the pulley is a cylindrical, solid disk of mass
M = 5 kg, the angular acceleration of the pulley is closest to
(a) 0.2 rad s-2
(b) 2 rads-2
(c) 4 rads-2
(d) 20 rad s-2
(e) 40 rad s-2
6. During a pirouette a figure skater reduces her moment of inertia from I = 1.24 kg m2
to I2 = 0.25 kg m? by pulling in her arms. If she rotates with an angular speed of
wi = 0.5 rad s-1, before pulling in her arms, what is her final angular speed when she
finished the process?
(a) 2.48 rad s-2
(b) 0.10 rad s-2
(c) 0.40 rad s-2
(d) 9.92 rad s-2
(е) 0.50 гаd s-2
7. A solid disk and a thin-walled ring of the same mass and radius roll down an incline.
starting from rest and from the same height. Which of these objects will reach the
bottom of the incline with a higher speed?
(a) The ring.
(b) The disk.
(c) Both will reach the bottom with the same speed.
95](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95d9a246-e90c-41bd-9705-9a4f0fbd3c96%2F3a290bb8-0721-4816-8f04-cddf41e4978c%2Fzg3dxld_processed.jpeg&w=3840&q=75)
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