Physics: Angular Acceleration of Rotational Objects
Physics

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A bicycle wheel has a diameter of 63.8 cm and a mass of 1.79 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire.
(a) What force must be applied by a chain passing over a 8.92cmdiameter sprocket in order to give the wheel an acceleration of 4.49 rad/s2? (b) What force is required if you shift to a 5.65cmdiameter sprocket?
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Torque = Inertia x alpha (angular acceleration rad/s^2)
Torque also equals force x radius
First of all lets find the inertia of the wheel.
hoop = mr^2 = 1.79 x 0.319^2 = 0.18215kgm^2
Now, Torque = 0.18215 x 4.49= 0.8178/radius= force
0.8178 x 0.0446 =36.47N
What force must be applied to attain acc of 4.49 rad/s^2?
17.33 N
117 N x 0.316 m = 36.972 Nm
36.972/ 0.0446 = 828.96 N
Total = 17.33 + 828.96= 846.29 N (answer)
What force is required if the chain shifts to a 5.65 cm diameter sprocket?
the torque is the same and divide by the radius
The answer comes out to be 1390.9 N
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