Question

The angular velocity of a wheel is 70 rad/s. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is:
(A) 70 m/s
(B) 35 m/s
(C) 30 m/s
(D) 20 m/s

Answer 1

Hint: To answer this question we should be knowing the formula to find the linear velocity. This formula involves the relationship between the angular velocity of the wheel and the radius of the wheel. We have to put the values in the formula and then we can obtain the answer to this question.

Complete step by step answer:
As it is given in the question that the value of w is 70 rad/s. Here w signifies the angular velocity of the wheel. The radius of the wheel is given by r. The value of r as per the question is 0.5 m.
So we know that the formula of linear velocity is given by:
Linear velocity or v = angular velocity $ \times $ radius
$ \Rightarrow v = w \times r$
We have to put the values in the equation mentioned above to get that:
$
  v = 0.5 \times 70 \\
   \Rightarrow v = 35m/s \\
 $
So we can say that the value of the linear velocity of the wheel is 35 m/s.

Hence option B is correct.

Note: In this question, we have come across the term of linear velocity. For a better understanding we have to know the meaning of this term. By linear velocity we mean the measurement of change of the position of a specific object that is in motion along a straight line. It should also be known to us that any object that is motion will be having a linear velocity.