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Fundamentals Of Physics
Found in: Page 293

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Short Answer

The flywheel of an engine is rotating at 25.0rads . When the engine is turned off, the flywheel slows at a constant rate and stops in 1.0 s . Calculate

(a) The angular acceleration of the flywheel,

(b) The angle through which the flywheel rotates in stopping, and

(c) The number of revolutions made by the flywheel in stopping

  1. Angular acceleration of the flywheel is - 1.25rads2.
  2. Angle through which the flywheel rotates is 250 rad
  3. Number of revolutions made by the flywheel is 39.8 rev
See the step by step solution

Step by Step Solution

Step 1: Given

  1. Flywheel rotation is 25 rad/sec
  2. Flywheel stops in 20 sec

Step 2: Determining the concept

Here, initial and final angular velocity and time are given. Using the angular kinematic equations, find angular acceleration and angle. Convert the angle into revolutions by using the relationship between the radians traced in one rotation.

Formulae are as follow:

ω=ω0+αt

θ=ω+ω02×t

Where,

t is time, ω,ω0 are final and initial angular velocities, is angular acceleration and θ is displacement.

Step 3: (a) determining the angular acceleration of the flywheel

Using the angular kinematic equation,

ω=ω0+αt0=25+α×20α=-1.25 rad/ s2

Hence, angular acceleration of the flywheel is - 1.25rads2

Step 4: (b) Determining the angle through which the flywheel rotates

The angular displacement can be found as,

θ=ω+ω02tθ=252×2θ=250 rad

Hence, angle through which the flywheel rotates is 250 rad

Step 5: (c) Determining the number of revolutions made by the flywheel

Convert angular displacement into number of rotations as,

n=250 rad×1 rev2×π n=39.8 rev

Hence, number of revolutions made by the flywheel is 39.8 rev.

Therefore, basic formulas of rotational kinematics can be used to find angular acceleration, angle, and number of revolutions.

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