Discuss Concept Problem 1 1. Two wheels with fixed axles, each having a mass of

Question

Discuss Concept Problem 1 1. Two wheels with fixed axles, each having a mass of m (mi-m2 = m), start from rest with forces applied as shown. 2 Assume moments of inertia to be 1/2 m R 2 and 1/2 m2 R2 respectively. If R2 2R1 describe F2 in terms of F1 when both wheels have the same angular acceleration. Obviously, there is friction between the surface and the wheels. How would you determine the magnitude of that friction? Assume a friction coefficient between the wheel and the surface: When would the force be large enough for the wheels to slip? What happens when the force F acts at the center of mass or even lower? mi, Ki m2, R2

Explanation / Answer

Given,

I1 = 1/2 m R1^2 ; I2 = 1/2 m2 R2^2

R2 = 2 R1 ; m1 = m2 = m

we know that,

torque = I alpha = R F

alpha = R F/I

since they have same alpha

R1 F1/I1 = R2 F2/I2

F2 = (R1/R2)(I2/I1) F1

I2/I1 = 1/2 m 4R1^2/1/2 m R1^2 = 4

F2 = (R1/2R1) x 4 F1 = 2 F1

Hence, F2 = 2 F1

frictional force is:

Ff = u N

N = F2 - F1

Ff = u (F2 - F1)

No torque will be produced if F acts at the COM.

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