Question

The maximum speed of a wheel is 450 rpm.If it is running at 80 % its maximum speed then angle it runs through in 1 second is k pi.Find k.

Answer 1

Given :

• The maximum speed of a wheel is 450 rpm
• If it is running at 80 % its maximum speed then angle it runs through in 1 second is kπ

To find : Value of k.

Solution :

The value of k is 12

We can simply solve this numerical problem by using the following process. (here, our goal is to use existing formulas for numerical problems in order to calculate the value of k)

Maximum speed = 450 rpm

The wheel is running at = 450 × 80/100 = 360 rpm

The angular velocity ω can be written as,

ω = (2πn)/60

ω = (2π × 360)/60

ω = 12π rad/s

[In above mentioned calculation, 'n' is the rotational speed in rpm.]

The angle it runs,

θ = ωt

In this case, time (t) = 1 second

So,

θ = (12π rad/s) × (1 s) = 12π rad

Now, as per the data mentioned in the question

θ = kπ rad

And, as per our calculation,

θ = 12π rad

So, by comparing two values of θ, we get :

kπ = 12π

k = 12

(This will be considered as the final result.)

Hence, value of k is 12