4. (15) A wheel starts from rest and rotates with constant angular acceleration

Question

4. (15) A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of 11.4 rad/s in 2.96 a) Find the magnitude of the angular acceleration of the wheel b) Find the angle in radians through which it rotates in this time interval c) The diameter of this wheel is 30 cm. without slipping? What linear distance does the wheel travel if it rolls Extra Credit: (3)I have a slender rod, mass 'M', length 'L'. I want to spin it so that it has the smallest possible moment of inertia. Draw where the axis of rotation should be for the smallest moment of inertia.

Explanation / Answer

Given,

w0 = 0 rad/s ; w = 11.4 rad/s ; t = 2.96 rad/s

a)We know from eqn in circular motion

w = w0 + alpha t

alpha = (w - w0)/t = (11.4 - 0)/2.96 = 3.85 rad/s^2

Hence, alpha = 3.85 rad/s^2

b)We know from eqn in circular motion

theta = w0 t + 1/2 alpha t^2

theta = 0 x 2.96 + 0.5 x 3.85 x 2.96^2 = 16.87 rad

Hence, theta = 16.87 rad

c)d = 30 cm => r = 15 cm = 0.15 m

v = r w = 0.15 x 11.4 = 1.71 m/s

a = 1.71/2.96 = 0.58 m/s^2

S = ut + 1/2 at^2

S = 0 + 0.5 x 0.58 x 2.96^2 = 2.54 m

Hence, S = 2.54 m

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