A 45.0-cm diameter disk rotates with a constant angular acceleration of 2.50 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. At t = 2.30 s, find (a) the angular speed of the wheel, (b) the linear speed and tangential acceleration of P, and (c) the position of P (in degrees, with respect to the positive x-axis).
here,
the angular acceleration , alpha = 2.5 rad/s^2
theta0 = 57.3 degree = 0.9997 rad
diameter , d = 45 cm
radius , r = d/1 = 22.5 cm = 0.225 m
at t = 2.3 s
a)
the angular speed of the wheel , w = w0 + alpha * t
w = 0 + 2.5 * 2.3 rad/s
w = 5.75 rad/s
b)
the linear speed , v = r * w
v = 0.225 * 5.75 m/s = 1.29 m/s
the tangential acceleration , a = alpha * r
alpha = 2.5 * 0.225 rad/s^2 = 0.56 m/s^2
c)
the angle covered, theta = theta0 + (w0 * t + 0.5 * alpha * t^2)
theta = 0.9997 + ( 0 + 0.5 * 2.5 * 2.3^2) rad
theta = 7.61 rad = 436.4 degree
the angle with positive x-axis , phi = (436.4 - 360) degree
phi = 76.4 degree
A 45.0-cm diameter disk rotates with a constant angular acceleration of 2.50 rad/s2.
A 36.2-cm diameter disk rotates with a constant angular acceleration of 2.8 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. rad/s (b) Find the linear velocity and tangential acceleration of P at t =...
A 47.4-cm diameter disk rotates with a constant angular acceleration of 2.80 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. rad/s (b) Find the linear velocity and tangential acceleration of P at t =...
A 39.2-cm diameter disk rotates with a constant angular acceleration of 2.8 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. rad/s 2.30 s (b) Find the linear velocity and tangential acceleration of P at t...
A 40.0-cm diameter disk rotates with a constant angular acceleration of 2.70 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) At t 2.50 s, find the angular speed of the wheel. rad/s (b) At t 2.50 s, find the magnitude of the linear velocity and tangential acceleration...
A 41.0-cm diameter disk rotates with a constant angular acceleration of 2.80 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) At t = 2.50 s, find the angular speed of the wheel. ______??____rad/s (b) At t = 2.50 s, find the magnitude of the linear velocity...
A wheel 2.50 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 3.55 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find the following. (a) the angular speed of the wheel 7.1 rad/s (b) the tangential speed of the point P (c)...
0, and a line drawn from the center of the disk to a point on the A 51.5-cm diameter disk rotates with a constant angular acceleration of 2.3 rad/s. It starts from rest at 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. rad/s mus (b) Find the linear velocity and tangential acceleration of Patt-2.30 S. linear velocity tangential acceleration...
A wheel of diameter 30.0 cm starts from rest and rotates with a constant angular acceleration of 2.50 rad/s2. At the instant the wheel has completed its second revolution, compute the radial acceleration of a point on the rim in two ways. Using the relationship arad = ω2r. From the relationship arad = v2/r.
A wheel 2.30 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.50 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find the following. (a) the angular speed of the wheel rad/s (b) the tangential speed of the point...
A wheel 2.10 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 3.50 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find the following. (a) the angular speed of the wheel (b) the tangential speed of the point P...