Answer :
Final answer:
The linear speed of a wheel with a radius of 15 cm rotating at 20 rpm is approximately 0.31 m/s when converted and calculated using the relationship between linear speed, radius, and angular velocity.
Explanation:
To calculate the linear speed of a wheel, you can use the relationship between linear speed (v), the radius (r) of the wheel, and its angular velocity (ω). The formula is v = r ω, where v is the linear speed, r is the radius, and ω is the angular velocity in radians per second. In this case, the wheel's radius is 0.15 meters (since 15 cm equals 0.15 meters), and it is rotating at 20 revolutions per minute (rpm).
First, let's convert rpm to radians per second:
- 1 revolution is 2π radians
- 20 rpm is therefore 20 * 2π radians per minute
- Which is (20 * 2π)/60 radians per second (since there are 60 seconds in a minute)
Now, we can calculate the angular velocity in radians per second:
- ω = (20 * 2π)/60
- ω = (20 * 2 * 3.14159)/60
- ω = 2.0944 radians/second
Finally, we find the linear speed by multiplying the radius by the angular velocity:
- v = r ω = 0.15 m * 2.0944 rad/s
- v ≈ 0.31416 m/s
- Rounding to two decimal places, v ≈ 0.31 m/s
None of the answer choices A) 1.57 m/s, B) 3.14 m/s, C) 4.71 m/s, D) 6.28 m/s match the value we found. Hence, there might be a mistake in the answer choices provided.
