Question

A wheel of 0.5 m radius rolls without slipping on a horizontal surface. The axle of the wheel advances at constant velocity, moving a distance of 20 m in 5 s. The angular speed of the wheel about its point of contact on the surface is:

Answer 1

Answer:

3.2 rad/sec

Step-by-step explanation:

Given;

Distance s = 20m

Time, t = 5s

Radius, r = 0.5m

For a circular motion, Acceleration,  a = rω             ------- (1)

From equation of motion, $s = ut + \frac{1}{2}at^{2}$

The wheel is starting from rest, initial velocity u = 0

                        ∴ $s = \frac{1}{2}at^{2}$

                           $20 = \frac{1}{2}a5^{2}$

                           $20 = \frac{1}{2}25a$

                           25a = 20 × 2

                           25a =40

                           $a = \frac{40}{25}$

                           Acceleration,  a = 1.6 m/s²

Substituting the values of a and r into equation (1)

                           16 = 0.5ω

                           ω = 3.2 rad/sec

The angular speed of the wheel about its point of contact on the surface is 3.2 rad/sec.