The flywheel of a steam engine runs with a constant angular speed of 164 rev/min. When steam is shut off, the friction of the bearings and the air brings the wheel to rest in 1.6 h. I figured out the constant angular acceleration=1.71 rev/min2 but im not sure how to find:What is the magnitude of the tangential component of the linear acceleration of a particle that is located at a distance of 44 cm from the axis of rotation when the flywheel is turning at 82.0 rev/min
physics - bobpursley, Monday, September 27, 2010 at 7:29pm
linear acceleration=1.71/min^2, I certainly would change that to rad/sec^2
, time radius
tangential acceleration=angularacceleration*radius. Since angular acceleration is constant, it does not matter what angular velocity is.
physics - Anonymous, Tuesday, September 28, 2010 at 6:55pm
i did what you told me but it was incorrect, did i make a mistake:
1.71/min^2*(pi/30)=0.179rad/s/s
(0.179rad/s/s)*44cm=7.876cm/s/s
To find the magnitude of the tangential component of the linear acceleration, you will need to use the equation:
tangential acceleration = angular acceleration * radius
First, let's convert the angular acceleration from rev/min^2 to rad/s^2.
Given: angular acceleration = 1.71 rev/min^2
To convert rev/min^2 to rad/s^2, we need to multiply by 2π/60 (since there are 2π radians in one revolution and 60 seconds in one minute).
angular acceleration in rad/s^2 = (1.71 rev/min^2) * (2π/60) = 0.179 rad/s^2
Now we can use this angular acceleration and the given radius (44 cm) to find the tangential acceleration.
tangential acceleration = (0.179 rad/s^2) * 44 cm
Note that the units of cm cancel out, since we are multiplying by cm.
tangential acceleration = 7.876 cm/s^2
So, the magnitude of the tangential component of the linear acceleration of a particle located 44 cm from the axis of rotation when the flywheel is turning at 82.0 rev/min is 7.876 cm/s^2.
The formula for tangential acceleration is given by the formula:
tangential acceleration = angular acceleration * radius.
You correctly found the angular acceleration to be 1.71 rev/min^2. However, in order to use this value in the formula, it should be converted to rad/s^2, since the units for angular acceleration are typically expressed in rad/s^2. To convert from rev/min^2 to rad/s^2, you can use the conversion factor of 2π rad/rev and 1 min = 60 s.
So, the correct conversion is:
1.71 rev/min^2 * (2π rad/rev) * (1/60 min/s) = 0.179 rad/s^2
Now, you can use the updated value of angular acceleration in the formula to calculate the tangential acceleration.
tangential acceleration = 0.179 rad/s^2 * 44 cm = 7.876 cm/s^2
Therefore, the magnitude of the tangential component of the linear acceleration is 7.876 cm/s^2.