An electric motor rotating a grinding wheel at 100 rev/min is switched off. With constant negative angular acceleration of magnitude 2rad/second squared, how long does it take the wheel to stop?
100 * 2π / 60 / 2 sec
To find out how long it takes for the grinding wheel to stop, we need to determine the time taken for the wheel to reach zero angular velocity.
We are given the initial angular velocity (ω₀) of the grinding wheel as 100 rev/min, which can be converted into radians per second:
ω₀ = 100 rev/min = 100 * 2π rad/60 sec = 10π/3 rad/sec.
We are also given the magnitude of negative angular acceleration (α) as 2 rad/s².
To find the time taken for the wheel to stop (t), we can use the following equation of motion for rotational motion:
ω = ω₀ + αt,
where ω is the final angular velocity.
Since the wheel stops when the angular velocity becomes zero (ω = 0), we can rewrite the equation as:
0 = ω₀ + αt.
Substituting the given values, we have:
0 = 10π/3 + 2t.
Now, we can solve for t:
2t = -10π/3,
t = (-10π/3) / 2,
t = -5π/3.
The negative value of time (-5π/3) indicates that the wheel will take 5π/3 seconds to stop rotating in the opposite direction.
Therefore, it will take approximately 5π/3 seconds for the grinding wheel to come to a complete stop.