Question

 A point on the outer surface of rim of the wheel 3 m in diameter has linear velocity of 18 ms⁻¹ The angular velocity of the wheel is *

(a) 54 rad s⁻¹

(b) 6 rad s⁻¹

(c) 12 rad s⁻¹

(d) 7 rad s⁻¹​

Answer 1

Option (c) 12 rad s-¹

To Find :-

• The angular velocity of the wheel.

Solution :-

Given,

• Diameter (d) = 3 m
• Linear velocity (v) = 18 ms-¹

⟶ Radius (r) = d/2

⟶ r = 3/2

⟶ r = 1.5 m

As we know that,

v = ωr

Here,

• v = velocity
• ω = angular velocity
• r = radius

We need to find angular velocity,

ω = v/r

[ Put the values ]

⟶ ω = 18/1.5

⟶ ω = 12 rad s-¹

Therefore,

The angular velocity of the wheel is 12 rad s-¹.