Aflywheel with radius 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2. for a point on the rim of the flywheel, what are the magnitudes of the tangential, radial, and resultant accelerations after 2.00 s of acceleration

at = 0.18 m/s²

ac = 0.432 m/s²

a = 0.468 m/s² m/s²

Explanation:

Tangential acceleration is calculated as follows:

at = α*R     Formula (1)

Centripetal  or radial acceleration is calculated as follows:

ac =ω²*R   Formula (2)

We apply the equations of circular motion uniformly accelerated :

ωf= ω₀ + α*t  Formula (3)

Where:

α : angular acceleration (rad/s²)

t : time interval (s)  

ω₀ : initial angular speed ( rad/s)

ωf : final angular speed  ( rad/s)

R : radius of the circular path (m)

at:  tangential acceleration, (m/s²)

ac: centripetal acceleration, (m/s²)

Data:

R = 0.3 m  : radius of the flywheel

ω₀ = 0

α = 0.6 rad /s²

t = 2 s

Calculation of  ωf at t= 2 s

We apply the Formula (3) :

ωf= ω₀ + α*t  

ωf= 0 + ( 0.6)*(2)

ωf =1.2 rad/s

Calculation of the tangential acceleration

We apply the Formula (1)

at = α*R =  ( 0.6)*(0.3) = 0.18 m/s²

Calculation of the radial acceleration

We apply the Formula (2)

ac =ω²*R  = (  1.2)²*(0.3) = 0.432 m/s²

Calculation of the resultant acceleration (a)

a= 0.468 m/s²