Question

A turntable rotates at 68 revolutions per minute. What is its angular speed in radians per second?

Answer 1

`\displaystyle (34 \pi)/(15) \ (rad)/(sec)`

General Formulas and Concepts:

Math

• Dimensional Analysis

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Pre-Calculus

• Angular Speed: 2π rad per revolution

Explanation:

Step 1: Define

68 revolutions per minute

Step 2: Identify Conversions

2π rad per revolution

60 seconds = 1 minute

Step 2: Convert

1. [DA] Set up:
   `\displaystyle (68 \ rev)/(1 \ min) \cdot (2 \pi \ rad)/(1 \ rev) \cdot (1 \ min)/(60 \ sec)`
2. [DA] Multiply/Divide [Cancel out units]:
   `\displaystyle (34 \pi)/(15) \ (rad)/(sec)`