Question

Q13. A simple wheel and axle has wheel and axle
of diameters of 300mm and 30mm
respectively. Find its velocity ratio
(A) 10
(B) 20
(C) 15
(D) 40​

Answer 1

Answer:

The velocity ratio will be 11:10.

Step-by-step explanation:

When a wheel rotates, the velocity of wheel must be angular velocity.

Angular Velocity: The rate of rotation of an object around a fixed point/axis is called angular velocity. This is denoted by the symbol 'ω'.

• 'ω' is a vector quantity. Its unit is radian/second (rad/s).
• The formula for angular velocity is, ω = $\frac{v}{r}$

        v is the linear velocity and r is the radius.

• Solution: Suppose linear velocity for both wheels = v

        For simple wheel, diameter = 300 mm

                                        radius = r = 300/2 = 150 mm

                                        Angular velocity, ω1 = $\frac{v}{150}$ rad/s

        For wheel with axle, diameter = 300 + 30 mm = 330 mm

                                        radius = r = 330/2 = 165 mm

                                        Angular velocity, ω2 = $\frac{v}{165}$ rad/s

       The ratio of angular velocity, ω1 : ω2 = $\frac{v}{150}$ : $\frac{v}{165}$

                                                                      = 165/150 = 11 : 10