Question

A wheel rotates at 50 rpm about its axis. The angular retardation that can stop the wheel in one minute is​

Answer 1

Answer:

yeah I got 6 points yeah thank you

Answer 2

Given:

The frequency of the wheel = 50 rpm

Time taken by the wheel to stop = 60s

To Find:

The angular retardation of the wheel

Solution:

What is angular retardation?

• The acceleration of a rotating body in the direction opposite to its angular velocity is called angular retardation.
• It opposes the rotation of the body on its axis.

To find the angular retardation, we will follow these steps:

1. Find the initial angular velocity of the body.

We know that angular velocity = 2πf

           But angular frequency is in rpm

                           1 rpm = $\frac{1}{60}$ rps

                       ⇒  50 rpm = $\frac{50}{60}$ rps

                                      = $\frac{5}{6}$ rps

      Angular velocity = 2π × $\frac{5}{6}$

                                  = $\frac{5}{3}$ π rad/s

2. Apply the formula.

For this question, we know the following:

1. initial angular velocity (ω₁) = $\frac{5}3}$π rad/s
2. final angular velocity (ω₂) = 0
3. time = 60s
4. retardation (α) =?

       

                  So we can apply ω₂ = ω₁ + αt               (1)

3. Find angular retardation.

Substituting known values in (1):

                  ⇒  0 = $\frac{5}{3}$π + 60α

                  ⇒ 60α = -$\frac{5}{3}$ π

                  ⇒ α = -$\frac{1}{36}$ × 3.14 rad/s²

                  ⇒ α = -0.087 rad/s²

The negative sign shows the direction of acceleration.

Therefore, the correct answer is 0.087 rad/s².