Rotational Dynamics and Static Equilibrium. What is the angular accleration of the wheel?

The drive chain in a bicycle is applying a torque of 0.85Nm to the wheel of the bicycle. Treat the wheel as a hoop with a mass of 0.75kg and a radius of 33cm. What is the angular acceleration of the wheel?





(a) 10.4 rad/s^2


(b) 5.2 rad/s^2


(c) 3.43 rad/s^2


(d) 1.06 rad/s^2





How did you arrive at that answer?





Thnks

Rotational Dynamics and Static Equilibrium. What is the angular accleration of the wheel?
Torque is the product of a force and a lever arm. We have the torque as .85 newton*meters. We can get the answer by a simple dimensional analysis. A newton is actually a kilogram*meter / second^2. We have the length and the mass. So we just need the angular acceleration. Divide .85 N m by .33 m (not 33 cm), then divide this result by .75 kg.





This gives 3.43 rad / sec^2


So C is the correct answer.
Reply:ans is(c) t=Fd and if we consider r=d then a=t/md
Reply:You are told the wheel is a hoop and are given it's mass so they probably expect you to use the moment of inertia I of the wheel.





In this case, I = mR^2 where R is the radius of the wheel and m is the mass.





torque t = Ia where a is the angular acceleration.





I get 10.4 rad/s^2