The image above represents maximum velocity in circular motion. To calculate the maximum velocity, three essential parameters are needed and these parameters are** coefficient of friction (Î¼), radius (r) and acceleration due to gravity (g).**

The formula for calculating maximum velocity:

V_{max}Â = âˆš(Î¼gr)

Where;

V_{max} = maximum velocity

Î¼ = coefficient of friction

r = radius

g = acceleration due to gravity

Let’s solve an example;

Find the maximum velocity when the coefficient of friction is 14 with a radius of 7 and acceleration due to gravity of 9.8.

This implies that;

Î¼ = coefficient of friction = 14

r = radius = 7

g = acceleration due to gravity = 9.8

V_{max}Â = âˆš(Î¼gr)

V_{max}Â = âˆš(14 x 7 x 9.8)

So, V_{max}Â = âˆš(960.40)

V_{max}Â = 30.99

Therefore, the **maximum velocity** is **30.99 m/s.**

**Calculating the Coefficient of Friction when the Maximum Velocity, Radius and Acceleration due to Gravity is Given**

Î¼ = ^{Vmax2} / _{gr}

Where;

Î¼ = coefficient of friction

V_{max} = maximum velocity

r = radius

g = acceleration due to gravity

Let’s solve an example;

Find the coefficient of friction with a maximum velocity of 120, radius of 15, and acceleration due to gravity is 9.8.

This implies that;

V_{max} = maximum velocity = 120

r = radius = 15

g = acceleration due to gravity = 9.8

Î¼ = ^{Vmax2} / _{gr}

Î¼ = ^{1202} / _{15 x 9.8}

Then, Î¼ = ^{14400} / _{147}

Î¼ = 97.96

Therefore, the **coefficient of friction** is **97.96.**

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**Calculating the Radius when the Maximum Velocity, Coefficient of Friction and Acceleration due to Gravity are Given**

r = ^{Vmax2} / _{gÎ¼}

Where;

r = radius

V_{max} = maximum velocity

Î¼ = coefficient of friction

g = acceleration due to gravity

Let’s solve an example;

Find the radius with a maximum velocity ofÂ 90, coefficient of friction of 24 and acceleration due to gravity is 9.8?

This implies that;

V_{max} = maximum velocity = 90

Î¼ = coefficient of friction = 24

g = acceleration due to gravity = 9.8

r = ^{Vmax2} / _{gÎ¼}

r = ^{902} / _{9.8 x 24}

Then, r = ^{8100} / _{235.2}

r = 34.44

Therefore, the **radius** is **34.44.**

**How to Calculate Maximum Velocity Using Nickzom Calculator**

Nickzom Calculator â€“Â **The Calculator Encyclopedia** is capable of calculating the maximum velocity.

To get the answer and workings of the maximum velocity using the **Nickzom Calculator â€“ The Calculator Encyclopedia**, you need to obtain the app.

You can get this app via any of these means:

**Web**Â â€“Â https://www.nickzom.org/calculator-plus

To get access to theÂ **professionalÂ **version via web, you need toÂ **register**Â andÂ **subscribeÂ **for**Â NGN 1,500Â **per**Â annum**Â to have utter access to all functionalities.

You can also try theÂ **demoÂ **version viaÂ https://www.nickzom.org/calculator

**Android (Paid)**Â â€“Â https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)**Â â€“Â https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)**Â â€“Â https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to theÂ **Calculator Map,Â **then click onÂ **MechanicsÂ **underÂ **Engineering**

Now, Click onÂ **Motion of Circular PathÂ **underÂ **Mechanics**

Click on **Maximum Velocity****Â **underÂ **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the maximum velocity according to the respective parameter which are the **coefficient of friction (Î¼)**,** radius (r)** and** acceleration due to gravity (g)****.**

Now, enter the value appropriately and accordingly for the parameter as required by the **coefficient of friction (Î¼)** is **14**,** radius (r)** is **7 **and** acceleration due to gravity (g)Â **isÂ **9.8.**

Finally, Click on Calculate

As you can see from the screenshot above,Â **Nickzom Calculator** â€“ The Calculator Encyclopedia solves for the maximum velocity and presents the formula, workings, and steps too.