A bicycle wheel has a diameter of 700mm and a mass of 3.0 kg. Most of the mass of the wheel is in the tire so you can treat it as a hoop.

a) Suppose the wheel is attached to a bicycle that is moving at 7.0 m/s. What is the angular velocity of the wheel in rad/sec?

b) If the bicycle slows down to 4.0 m/s over a period of 10.0 sec, what is the angular acceleration of the wheel in rad/sec 2?

A bicycle wheel has a diameter of 63.8 cm and a mass of 1.82 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 116 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 9.09-cm-diameter sprocket in order to give the wheel an acceleration of 4.41 rad/s^{2}?

?N

?N

(b) What force is required if you shift to a 5.55-cm-diameter sprocket?

? kN

A bicycle wheel has a diameter of 700mm and a mass of 3.0 kg. Most of the mass of the wheel is in the tire so you can treat it as a hoop. It is taken off the bicycle and put on a test stand where it can rotate by itself without being connected to the rest of the bicycle.

a) How much torque would it take to make the wheel speed up from rest to 1.5 rev/sec in 10 sec?

b) Now let’s suppose that the wheel is still on the test stand and the torque is being delivered to the wheel by pulling on a chain that goes around a gear on the same axis as the wheel (it works like how the chain powers the rear wheel of a normal bicycle). The gear has a diameter of 12.5 cm. How much tension would you have to put on the chain to make the wheel speed up from rest to 1.5 rev/sec in 10 sec?

A bicycle wheel has a diameter of 63.2 cm and a mass of 1.88 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 121 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 9.05-cm-diameter sprocket in order to give the wheel an acceleration of 4.47 rad/s^{2}? Answer in Newtons.

(b) What force is required if you shift to a 5.50-cm-diameter sprocket?

Answer in kN

A bicycle wheel has a diameter of 63.8 cm and a mass of 1.71 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 115 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 8.94-cm-diameter sprocket in order to give the wheel an acceleration of 4.55 rad/s^{2}?

(b) What force is required if you shift to a 5.64-cm-diameter sprocket?

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