Final answer:
The magnitude of the tangential acceleration, centripetal acceleration, and resultant acceleration of a point on the rim of a flywheel are 0.18 m/s², 0.365 m/s², and 0.408 m/s².
Step-by-step explanation:
The magnitude of the tangential acceleration can be calculated using the equation: tangential acceleration = angular acceleration * radius.
In this case, the radius is given as 0.3 m and the angular acceleration is given as 0.6 rad/s².
So, the tangential acceleration is 0.6 * 0.3
= 0.18 m/s².
The centripetal acceleration can be calculated using the equation: centripetal acceleration = (angular velocity)² * radius.
After the flywheel has turned through 1 rad, its angular velocity can be calculated using the equation: angular velocity = sqrt(2 * angular acceleration * angle).
In this case, the angle is given as 1 rad and the angular acceleration is given as 0.6 rad/s².
So, the angular velocity is sqrt(2 * 0.6 * 1) = 1.095 rad/s.
Substituting this value and the given radius of 0.3 m into the centripetal acceleration equation, we get:
centripetal acceleration = (1.095)² * 0.3
= 0.365 m/s².
The resultant acceleration at a point on the rim of the flywheel can be calculated using the formula:
resultant acceleration = sqrt(tangential acceleration² + centripetal acceleration²).
Substituting the previously calculated values, we get: resultant acceleration
= sqrt(0.18² + 0.365²)
= 0.408 m/s².