Question

part 9 - mechanical comprehension question 12 of 15 wheel a has a diameter of 6 inches, while wheel b has a diameter of 12 inches. if wheel a turns at a rate of 8 rpm, what will be the speed of wheel b? a 4 rpm b 8 rpm c 48 rpm d 96 rpm click the button or type the letter next to your answer.

Explanation:

Step1: Recall the relationship between diameter and rotational speed for wheels connected by a belt (linear speed is equal)

The linear speed \( v \) of a wheel is given by \( v = \pi d n \), where \( d \) is the diameter and \( n \) is the rotational speed (in rpm). Since the linear speeds of wheel A and wheel B are equal (because they are connected by a belt), we have \( \pi d_A n_A=\pi d_B n_B \). We can cancel out \( \pi \) from both sides, so \( d_A n_A = d_B n_B \).

Step2: Plug in the known values

We know that \( d_A = 6 \) inches, \( n_A = 8 \) rpm, and \( d_B = 12 \) inches. We need to solve for \( n_B \). Rearranging the formula \( d_A n_A = d_B n_B \) for \( n_B \), we get \( n_B=\frac{d_A n_A}{d_B} \).

Substituting the values: \( n_B = \frac{6\times8}{12} \).

Step3: Calculate the value of \( n_B \)

First, calculate the numerator: \( 6\times8 = 48 \). Then divide by the denominator: \( \frac{48}{12}=4 \) rpm.

Answer:

A. 4 rpm