what is the angular momentum (in kg · m2/s) of the spinning wheel about its axis in the air the moment the bike leaves the ground? (Assume the wheel can be approximated by a hoop rotating abo its center of mass that rolls without slipping before the jump. Enter the magnitude.)

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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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A mountain biker takes a jump in a race and goes airborne. The mountain bike is traveling at **12.5 m/s** before it goes airborne. If the mass of the front wheel on the bike is **950 g** and has a radius of **30 cm**, what is the angular momentum (in kg·m²/s) of the spinning wheel about its axis in the air the moment the bike leaves the ground? (Assume the wheel can be approximated by a hoop rotating about its center of mass that rolls without slipping before the jump. Enter the magnitude.)

[Input Box] kg · m²/s
Transcribed Image Text:A mountain biker takes a jump in a race and goes airborne. The mountain bike is traveling at **12.5 m/s** before it goes airborne. If the mass of the front wheel on the bike is **950 g** and has a radius of **30 cm**, what is the angular momentum (in kg·m²/s) of the spinning wheel about its axis in the air the moment the bike leaves the ground? (Assume the wheel can be approximated by a hoop rotating about its center of mass that rolls without slipping before the jump. Enter the magnitude.) [Input Box] kg · m²/s
### Wind Turbine Mechanics

The problem statement involves calculating mechanics properties for a wind turbine with given specifications.

---

#### Specifications:
- **Blade Length:** 50 meters
- **Maximum Rotation Rate:** 12 revolutions per minute (rev/min)

#### (a) Angular Momentum Calculation
- **Blade Mass:** 5,900 kg each
- **Number of Blades:** 3
- **Assumption:** Turbine blades are approximated as rods rotating about one end.

##### Task:
Calculate the angular momentum (in kg·m²/s) of the turbine at the given rotation rate.

##### Input Field:
- **Angular Momentum:** [       ] kg·m²/s

---

#### (b) Torque Calculation
- **Time to Reach Maximum Rotation Rate:** 5 minutes
- **Assumption:** Blades start from rest.

##### Task:
Calculate the torque (in N·m) required to rotate the blades to the maximum rotation rate.

##### Input Field:
- **Torque:** [       ] N·m

---

This educational problem aids in understanding the application of physics principles such as angular momentum and torque in the context of large-scale machinery like wind turbines.
Transcribed Image Text:### Wind Turbine Mechanics The problem statement involves calculating mechanics properties for a wind turbine with given specifications. --- #### Specifications: - **Blade Length:** 50 meters - **Maximum Rotation Rate:** 12 revolutions per minute (rev/min) #### (a) Angular Momentum Calculation - **Blade Mass:** 5,900 kg each - **Number of Blades:** 3 - **Assumption:** Turbine blades are approximated as rods rotating about one end. ##### Task: Calculate the angular momentum (in kg·m²/s) of the turbine at the given rotation rate. ##### Input Field: - **Angular Momentum:** [ ] kg·m²/s --- #### (b) Torque Calculation - **Time to Reach Maximum Rotation Rate:** 5 minutes - **Assumption:** Blades start from rest. ##### Task: Calculate the torque (in N·m) required to rotate the blades to the maximum rotation rate. ##### Input Field: - **Torque:** [ ] N·m --- This educational problem aids in understanding the application of physics principles such as angular momentum and torque in the context of large-scale machinery like wind turbines.
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