A 37.8-cm diameter disk rotates with a constant angular acceleration of 3.0 rad/

Question

A 37.8-cm diameter disk rotates with a constant angular acceleration of 3.0 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.
(a) Find the angular speed of the wheel at t = 2.30 s.


(b) Find the linear velocity and tangential acceleration of P at t = 2.30 s.
linear velocity
tangential acceleration

c) Find the position of P (in degrees, with respect to the positive x-axis) at t = 2.30s.

Explanation / Answer

diameter=37.8 cm radius r = 18.9 cm = 0.189 m, constantangular acceleration a = 3.00 rad/s2, initial angular velocity = 0, initial position of P= ?o = 57.3o = 1 rad At t = 2.30 s, a) the angularspeed of the wheel ? = at = 6.90 rad/s b) the linearvelocity of P: v = ?r = 1.3041 m/s tangentialacceleration of P: at = a * r = 0.567m/s2 c) ? = ?o +0.5at^2 = 8.935rad = 511.97 deg Finally It appears as 511.97 - 360 =151.97 deg

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