The blades in a blender rotate at a rate of 6500 rpm . When the motor is turned off during operation, the blade
slow to rest in 3.0 s . What is the angular acceleration as the blades slow down?
3 s

Question

The blades in a blender rotate at a rate of 6500 rpm . When the motor is turned off during operation, the blade
slow to rest in 3.0 s . What is the angular acceleration as the blades slow down?

3 s

UpStudy AI · Accepted Answer

To determine the angular acceleration of the blender blades as they slow down, let's follow these steps:

### **Given:**
- **Initial angular velocity ($$ \omega_0 $$)**: 6500 revolutions per minute (rpm)
- **Final angular velocity ($$ \omega $$)**: 0 rpm (since the blades come to rest)
- **Time ($$ t $$)**: 3.0 seconds

### **Objective:**
Calculate the **angular acceleration ($$ \alpha $$)**.

### **Step 1: Convert Angular Velocity from rpm to radians per second (rad/s)**

1. **Convert rpm to revolutions per second (rev/s):**
   $$
   \omega_0 = 6500 \, \text{rpm} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} = \frac{6500}{60} \, \text{rev/s} \approx 108.333 \, \text{rev/s}
   $$

2. **Convert rev/s to rad/s:**
   $$
   \omega_0 = 108.333 \, \text{rev/s} \times 2\pi \, \text{rad/rev} \approx 108.333 \times 6.28319 \, \text{rad/s} \approx 680.678 \, \text{rad/s}
   $$

### **Step 2: Calculate Angular Acceleration ($$ \alpha $$)**

Angular acceleration is defined as the change in angular velocity divided by the time taken for that change.

$$
\alpha = \frac{\Delta \omega}{\Delta t}
$$

Where:
- $$ \Delta \omega = \omega - \omega_0 = 0 - 680.678 \, \text{rad/s} = -680.678 \, \text{rad/s} $$
- $$ \Delta t = 3.0 \, \text{seconds} $$

Plugging in the values:

$$
\alpha = \frac{-680.678 \, \text{rad/s}}{3.0 \, \text{s}} \approx -226.893 \, \text{rad/s}^2
$$

### **Conclusion:**
The angular acceleration of the blender blades as they slow down is approximately **-226.9 rad/s²**.

**Answer:**  
The angular acceleration is approximately –226.9 rad s⁻².
The angular acceleration is approximately –226.9 rad s⁻².

The blades in a blender rotate at a rate of 6500 rpm . When the motor is turned off during operation, the blade
slow to rest in 3.0 s . What is the angular acceleration as the blades slow down?
3 s

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The blades in a blender rotate at a rate of 6500 rpm . When the motor is turned off during operation, the blade slow to rest in 3.0 s . What is the angular acceleration as the blades slow down? 3 s

Solución de inteligencia artificial de Upstudy

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Solución

Beyond the Answer

preguntas relacionadas

Latest Physics Questions

The blades in a blender rotate at a rate of 6500 rpm . When the motor is turned off during operation, the blade
slow to rest in 3.0 s . What is the angular acceleration as the blades slow down?
3 s