Question

a particle is moving at a speed of 12m/s on a circle of radius 2m. if the speed of the particle is increased to 15 m/s in 2 seconds, what is the angular acceleration produced?​

Answer 1

Answer: ACCELERATION= 1.5 m/s^2.

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Answer 2

Answer:

A particle is moving at a speed of 12m/s on a circle of radius 2m. if the speed of the particle is increased to 15 m/s in 2 seconds, the angular acceleration produced is $0.75rad/s^{2}$

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 $r=2m$

change in speed $v_{2} -v_{1}=15-12=3m/s$

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

⇒ $w_{2} -w_{1} =3/2=1.5rad/sec$

the time taken $t=2s$

the angular acceleration is $1.5/2=0.75rad/s^{2}$