A fan blade is rotating with a constant angular acceleration of +8.4 rad/s2. At what point on the blade, as measured from the axis of rotation, does the magnitude of the tangential acceleration equal that of the acceleration due to gravity?
9.8/8.4
answer: 1.16666
To find the point on the fan blade where the magnitude of the tangential acceleration equals that of the acceleration due to gravity, we need to use the formula for tangential acceleration and the formula for acceleration due to gravity.
The formula for tangential acceleration is given by:
at = r * α
where:
at is the tangential acceleration,
r is the distance from the axis of rotation,
and α is the angular acceleration.
The formula for acceleration due to gravity is:
ag = g
where:
ag is the acceleration due to gravity,
and g is the acceleration due to gravity constant, approximately equal to 9.8 m/s^2.
Since we are looking for the point on the blade where the magnitudes of tangential acceleration and acceleration due to gravity are equal, we can set at equal to ag:
r * α = g
Plugging in the values α = 8.4 rad/s^2 and g = 9.8 m/s^2, we can solve for r:
r * 8.4 = 9.8
r = 9.8 / 8.4
r ≈ 1.17 meters
Therefore, the distance from the axis of rotation to the point on the blade where the magnitudes of tangential acceleration and acceleration due to gravity are equal is approximately 1.17 meters.