A rotating wheel with diameter 0.800 m is speeding up with constant angular acceleration. The speed of a point on the rim of the wheel increases from 3.00 m/s to 6.00 m/s while the wheel turns through 4.00 revolutions. Required:
What is the angular acceleration of the wheel?

The angular acceleration of the wheel is 3.357rad/s²

Explanation:

Given;

Diameter of the wheel, d = 0.8 m

radius of the wheel, r = 0.4 m

initial velocity of the wheel, u = 3 m/s

final velocity of the wheel, v = 6 m/s

number of revolutions of the wheel, N = 4 rev.

Convert the linear velocity in m/s  to angular velocity in rad/s;

v = ωr

ω = v / r

initial angular velocity,

final angular velocity,

The angular acceleration of the wheel is calculated as;

where;

α is the angular acceleration (rad / s²)

θ is the angular rotation (rad)

θ = Number of revolutions x 2π rad/rev

  =  4 rev. x 2π rad/rev

  = 25.136 rad.

α = 3.357 rad/s²

Therefore, the angular acceleration of the wheel is 3.357rad/s²

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