please help-physics?

Question

A spinning bicycle wheel 65.0 cm in diameter is rotating at 2.00 rev/s and comes to rest in 15.0 s
(a) What is the angular acceleration of the wheel?
(b) If the wheel has a mass of 1.75 kg, what frictional force in its bearing has caused it to stop?

Answer 1

First convert 2 rev/s to rad/sec
12.56 rad/s

now using
ω=ω0+α*t
compute α by setting ω=0
0=12.56+α*15
α=-0.837

b) You say in the bearing, yet you do not provide the radius of the bearing.

The energy of the wheel gets converted to work done by friction, but we need the torque in this case to compute the magnitude of the force.

What I will provide is the torque times angular displacement as the work and that will be equal to starting KE of the wheel.

The wheel is closely approximated as having a moment of inertia of m*r^2
in this case
1.75*0.65/2
or 0.56875
The angular displacement is related to

θ=θ0+ω0*t+.5*α*t^2
since we are looking for the angular displacement while the wheel slows, θ0=0
θ=12.56*15-.5*0.837*15^2
θ=94.2 rad

T*94.2=.5*0.56875*12.56^2
solve for T (Torque)
T=0.476 N m

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