**Problem Statement: Angular Momentum in Circular Motion**A Formula One race car with a mass of 740.0 kg is speeding through a course in Monaco and enters a circular turn at a speed of 235.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 190.0 km/h, also in the counterclockwise direction. The radius of curvature of the first turn is 125.0 m, and that of the second is 100.0 m. Compare the angular momenta of the race car in each turn taken about the origin of the circular turn. (Compare using the magnitudes of the angular momenta for each turn.)**Given:**- Mass of the car, \( m = 740.0 \, \text{kg} \)- Speed in turn 1, \( v_1 = 235.0 \, \text{km/h} \)- Speed in turn 2, \( v_2 = 190.0 \, \text{km/h} \)- Radius of turn 1, \( r_1 = 125.0 \, \text{m} \)- Radius of turn 2, \( r_2 = 100.0 \, \text{m} \)**Task:**Compare the angular momenta \( \frac{I_{\text{turn 1}}}{I_{\text{turn 2}}} \).---**Explanation of Elements:**This problem involves physics concepts related to circular motion and angular momentum. The task is to determine the ratio of angular momenta when the race car takes two different turns with specified radii and speeds. The angular momentum \( L \) in a circular motion setup is calculated using the formula:\[L = m \cdot v \cdot r\]where:- \( L \) is the angular momentum,- \( m \) is the mass of the object,- \( v \) is the tangential velocity,- \( r \) is the radius of the circle.The calculation requires converting the speeds from km/h to m/s and applying the formula for each turn to find the angular momenta. Finally, the ratio of these values provides the comparison requested.

mass of car(m)=740 kg speed of car for first turn(v1)=235 km/h=235×518 m/s=65.2777 m/s speed of car…

A Formula One race car with mass 740.0 kg is speeding through a course in Monaco and enters a circular turn at 235.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 190.0 km/h also in the counterclockwise direction. If the radius of curvature of the first turn is 125.0 m and that of the second is 100.0 m, compare the angular momenta of the race car in each turn taken about the origin of the circular turn. (Compare using the magnitudes of the angular momenta for each turn.) Iturn 1= turn 2

A Formula One race car with mass 740.0 kg is speeding through a course in Monaco and enters a circular turn at 235.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 190.0 km/h also in the counterclockwise direction. If the radius of curvature of the first turn is 125.0 m and that of the second is 100.0 m, compare the angular momenta of the race car in each turn taken about the origin of the circular turn. (Compare using the magnitudes of the angular momenta for each turn.) Iturn 1= turn 2

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

**Problem Statement: Angular Momentum in Circular Motion**

A Formula One race car with a mass of 740.0 kg is speeding through a course in Monaco and enters a circular turn at a speed of 235.0 km/h in the counterclockwise direction about the origin of the circle. At another part of the course, the car enters a second circular turn at 190.0 km/h, also in the counterclockwise direction. The radius of curvature of the first turn is 125.0 m, and that of the second is 100.0 m. Compare the angular momenta of the race car in each turn taken about the origin of the circular turn. (Compare using the magnitudes of the angular momenta for each turn.)

**Given:**

- Mass of the car, \( m = 740.0 \, \text{kg} \)
- Speed in turn 1, \( v_1 = 235.0 \, \text{km/h} \)
- Speed in turn 2, \( v_2 = 190.0 \, \text{km/h} \)
- Radius of turn 1, \( r_1 = 125.0 \, \text{m} \)
- Radius of turn 2, \( r_2 = 100.0 \, \text{m} \)

**Task:**

Compare the angular momenta \( \frac{I_{\text{turn 1}}}{I_{\text{turn 2}}} \).

---

**Explanation of Elements:**

This problem involves physics concepts related to circular motion and angular momentum. The task is to determine the ratio of angular momenta when the race car takes two different turns with specified radii and speeds. The angular momentum \( L \) in a circular motion setup is calculated using the formula:

\[
L = m \cdot v \cdot r
\]

where:
- \( L \) is the angular momentum,
- \( m \) is the mass of the object,
- \( v \) is the tangential velocity,
- \( r \) is the radius of the circle.

The calculation requires converting the speeds from km/h to m/s and applying the formula for each turn to find the angular momenta. Finally, the ratio of these values provides the comparison requested.

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