The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. Treat the wheel as a hoop with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel? A) 10.4 rad/s² B) 20.8 rad/s² C) 5.20 rad/s² D) 3.43 rad/s² E) 1.06 rad/s²

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The torque applied to the wheel is given by:$$ au = I \alpha$$where:$$ au$$ is the torque$$I$$ is the moment of inertia$$\alpha$$ is the angular accelerationThe moment of inertia of a hoop is given by:$$I = MR^2$$where:$$M$$ is the mass$$R$$ is the radiusSubstituting the given values into the equations, we get:$$0.850 ext{ Nm} = (0.750 ext{ kg})(0.330 ext{ m})^2 \alpha$$$$\alpha = 10.4 ext{ rad/s}^2$$Therefore, the angular acceleration of the wheel is 10.4 rad/s².

The Drive Chain in a Bicycle Is Applying a Torque