(a) Calculate the angular momentum (in kg-m²/s) of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.470 kg-m2. 17.7 v kg-m²/s (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia (in kg-m²) if his angular velocity drops to 2.40 rev/s. 1.175 v kg-m2 (c) Suppose instead he keeps his arms in and allows friction with the ice to slow him to 3.00 rev/s. What average torque (in N-m) was exerted this takes 18.0 seconds? 18.53 X N-m
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.
![### Physics Problem: Angular Momentum of an Ice Skater
#### (a) Calculating Angular Momentum
*Problem*: Calculate the angular momentum (in kg·m²/s) of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.470 kg·m².
*Answer*:
\[ \text{Angular Momentum} = 17.7 \, \text{kg·m²/s} \]
#### (b) Moment of Inertia After Reducing Spin Rate
*Problem*: He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia (in kg·m²) if his angular velocity drops to 2.40 rev/s.
*Answer*:
\[ \text{Moment of Inertia} = 1.175 \, \text{kg·m²} \]
#### (c) Average Torque Due to Friction
*Problem*: Suppose instead he keeps his arms in and allows friction with the ice to slow him to 3.00 rev/s. What average torque (in N·m) was exerted if this takes 18.0 seconds?
*Answer*:
\[ \text{Average Torque} = 18.53 \, \text{N·m} \, \text{(Incorrect answer)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb8ba6cb-f074-43c1-b7bc-05cc004f9981%2Fd0dec6bc-3658-44c9-9396-539886c0da1f%2Fd46mfy7_processed.png&w=3840&q=75)
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