Question

Multiple-Concept Example 10 provides one model for solving this type of problem. Two wheels have the same mass and radius of 4.5 kg and 0.43 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 12 rad in 9.5 s. Find the net external torque that acts on each wheel. (a) ?? = (b) ?? =

Answer 1

Since the wheels start from rest, angular acceleration, ?, is found using:
? =½?t²
(This is the rotational equivalent of s = ½at², used for straight line acceleration)

12 = ½ ? x 9.5²
? = 0.266 rad/s²
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Loop

Moment of inertia of loop = mr² = 4.5x0.43² = 0.832kgm²
Torque = moment of inertia x angular acceleration
? = I?
? = 0.832 x 0.266 = 0.221Nm = 0.22 Nm to 2 significant figures ......ANSWER
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Disc

Moment of inertia of solid disc ½mr². You should be able to see that because I has halved, the required torque halves. So the answer is 0.221/2 = 0.11 Nm to 2 significant figures)

Or you could work it out in full:
I = ½ x 4.5x0.43² = 0.416 kgm²
? = I? = 0.416 x 0.266 = 0.11 Nm to 2 significant figures.....ANSWER

Hope it will help.

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