Question

a body moves in a circle of radius 20cm at a speed that increases uniformly. if the speed changes from 5m/s to 6m/s in 2s find its angular acceleration

Answer 1

Answer:

A body moves in a circle of radius 20cm at a speed that increases uniformly. if the speed changes from 5m/s to 6m/s in 2s, its angular acceleration is $2.5 rad/s^{2}$

Explanation:

• The angular acceleration is the change in angular velocity divided by time to change

        $\alpha =\frac{w_{2} -w_{1} }{t_{2} -t_{1} }$

• In a circular motion, the linear velocity (V) and angular velocity (w) are related as,

        $V=rw$

        where r-radius of the circular path

From the question,

the radius of the circular path $r=20cm=0.2m$

change in speed $v_{2} -v_{1}=6-5=1m/s$

so the change in angular velocity $w_{2} -w_{1} =\frac{v_{2} -v_{1} }{r}$

⇒ $w_{2} -w_{1} =1/0.2=5rad/sec$

the angular acceleration is $5/2=2.5 rad/s^{2}$