The image above represents maximum velocity in circular motion.

To compute for the maximum velocity, three essential parameters are needed and these parameters are** coefficient of friction (μ), radius (r) and acceleration due to gravity (g).**

The formula for calculating maximum velocity:

V_{max} = √(μgr)

Where;

V_{max} = maximum velocity

μ = 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;

μ = coefficient of friction = 14

r = radius = 7

g = acceleration due to gravity = 9.8

V_{max} = √(μgr)

V_{max} = √(14 x 7 x 9.8)

V_{max} = √(960.40)

V_{max} = 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.**

μ = ^{Vmax2} / _{gr}

Where;

μ = 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

μ = ^{Vmax2} / _{gr}

μ = ^{1202} / _{15 x 9.8}

μ = ^{14400} / _{147}

μ = 97.96

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

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

r = ^{Vmax2} / _{gμ}

Where;

r = radius

V_{max} = maximum velocity

μ = coefficient of friction

g = acceleration due to gravity

Let’s solve an example;

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

This implies that;

V_{max} = maximum velocity = 90

μ = coefficient of friction = 24

g = acceleration due to gravity = 9.8

r = ^{Vmax2} / _{gμ}

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

r = ^{8100} / _{235.2}

r = 34.44

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

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the maximum velocity.

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

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

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

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

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

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Maximum Velocity**** **under **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 (μ)**,** 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 (μ)** is **14**,** radius (r)** is **7 **and** acceleration due to gravity (g) **is **9.8.**

Finally, Click on Calculate

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