Question

A flywheel with radius of 0.400 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Throwing a discus

Answer 1

Acceleration of of flywheel is 0.624 m/s^2

Acceleration is the rate of change of an object's velocity with respect to time. Acceleration is a vector quantity. The direction of an object's acceleration is given by the direction of the net force acting on that object

Solution:

Tangential acceleration is given by,

$a_{tan}$ = dv/dt

here, dt = time interval = 2.00 s

dv = change in linear speed of that point = Vf - Vi = (wf - wi)*r

r = radius of flywheel = 0.400 m

wf - wi = change in angular speed

from first rotational kinematics law,

wf - wi = α*dt

where,α= angular acceleration = 0.600 rad/s^2

then,

$a_{tan}$ = α*r*dt/dt = α*r

$a_{tan}$ = 0.600*0.400

$a_{tan}$ = 0.240 m/s^2

Radial acceleration is given by,

$a_{rad}$ = wf^2*r

here, again from first rotational kinematics law,

wf = wi +α*dt

wi = initial angular speed = 0 (As, starts from rest.)

then,

$a_{rad}$ = (wi +α*dt)^2*r

$a_{rad}$ = (0 + 0.600*2.00)^2*0.400

$a_{rad}$ = 0.576 m/s^2

As, radial and tangential acceleration are always perpendicular to each other then resultant acceleration will be:

a = sqrt(arad2 + atan2)

a = sqrt(0.576^2 + 0.24^2)

a = 0.624 m/s^2

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