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

Question

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

Answer 1

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.

Answer 2

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

Answer 3

To find the magnitude of the tangential component of the linear acceleration of a particle located at a distance of 44 cm from the axis of rotation when the flywheel is turning at 82.0 rev/min, you can use the following steps:

Step 1: Convert the angular velocity from revolutions per minute (rev/min) to radians per second (rad/s). Since there are 2π radians in one revolution and 60 seconds in one minute, the conversion factor is 2π/60.

Angular velocity (ω) in rad/s = (82.0 rev/min) × (2π/60) rad/s = 8.6 rad/s.

Step 2: Calculate the linear velocity (v) of the particle using the formula v = r × ω, where r is the distance from the axis of rotation. In this case, r = 44 cm = 0.44 m.

Linear velocity (v) = (0.44 m) × (8.6 rad/s) = 3.784 m/s.

Step 3: Calculate the tangential component of the linear acceleration (at) using the formula at = r × α, where α is the constant angular acceleration. In this case, α = 1.71 rev/min².

Angular acceleration (α) in rad/s² = (1.71 rev/min²) × (2π/60) rad/s² = 0.1785 rad/s².

Tangential component of linear acceleration (at) = (0.44 m) × (0.1785 rad/s²) = 0.07854 m/s².

Therefore, the magnitude of the tangential component of the linear acceleration of the particle located at a distance of 44 cm from the axis of rotation when the flywheel is turning at 82.0 rev/min is approximately 0.07854 m/s².