Question

A grind stone starts from rest and has a constant angular acceleration $3rad/s^2$. The radius of the grind stone is $0.5m$. The tangential speed of particle on the rim at the end of $2$ seconds is

• A. $2m/s$
• B. $5m/sec$
• C. $3m/sec$
• D. $6m/sec$

Answer 1

The correct option is C $3m/sec$

Given that grind stone starts from rest is rotating with constant angular acceleration $\alpha =3rad/s^2$

and the radius of grind stone $=r=0.5m$

given that

Initial conditions: Final conditions:

${\omega }_1=0rad/sec{t}_1=0sec$ ${\omega }_2=xrad/sec{t}_2=2sec$

Using the formula we get:

$\alpha =\frac{{\omega }_2-{\omega }_1}{t_2-t_1}$

$⟹3=\frac{x}{2}$

$⟹x=6rad/sec$

So FInal angular velocity ${\omega }_2=6rad/sec$

So tangential Speed = $v=r{\omega }_2=0.5\ast 6=3m/sec$