Question

Q1 The moment of inertia of a certain wheel about its axle is ?/? mR^2. The translational

speed of its axle after it starts from rest and rolls without slipping down an inclined

plane 2.13 m high is ?? I know the answe is 4.88m/s

A uniform cylinder (I =?/?mR^2) of diameter 0.20 m and mass 12 kg rolls without slipping

down a 37 degree inclined plane. The gain in translational kinetic energy of the cylinder

when it has rolled 5 m down the incline of the plane is approximately… ??? I know the answer is 3.9

Answer 1

1)

When the wheel is at the top of inclined plane, energy of wheel (potential energy)

When the wheel is at the bottom of inclined plane , energy of wheel (kinetic rotational and translational energy)

Since the wheel is rolling without slipping,

Moment of inertia of wheel about its axle is

Conserving the energy of wheel at top and bottom positions,

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2)

When the cylinder is at the top of inclined plane, energy of wheel (potential energy)

When the cylinder is at the bottom of inclined plane , energy of wheel (kinetic rotational and translational energy)

Since the cylinder is rolling without slipping,

Moment of inertia of cylinder about its axle is

Conserving the energy of wheel at top and bottom positions,

and given that

Translational kinetic energy at the bottom of the inclined plane is

( at the top)

Gain in translational kinetic energy of cylinder is

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