Question

In: Physics

A wheel has a mass of 0.5 kg and a radius of 0.25 m. It rolls...

A wheel has a mass of 0.5 kg and a radius of 0.25 m. It rolls such that the center of mass of the wheel has a velocity of 10 m/s.

a) Calculate the angular velocity of the wheel.

b) Calculate the translational kinetic energy of the wheel.

c) Calculate the rotational kinetic energy of the wheel.

d) Calculate the total kinetic energy of the wheel by summing the two kinetic energies

Solutions

Expert Solution

Mass of the wheel = M = 0.5 kg

Radius of the wheel = R = 0.25 m

Moment of inertia of the wheel = I

I = 1.5625 x 10^-2 kg.m²

Velocity of the center of mass of the wheel = V = 10 m/s

Angular velocity of the wheel =

= 40 rad/s

Translational kinetic energy of the wheel = E_T

E_T = 25 J

Rotational kinetic energy of the wheel = E_R

E_R = 12.5 J

Total kinetic energy of the wheel = E

E = E_T + E_R

E = 25 + 12.5

E = 37.5 J

a) Angular velocity of the wheel = 40 rad/s

b) Translational kinetic energy of the wheel = 25 J

c) Rotational kinetic energy of the wheel = 12.5 J

d) Total kinetic energy of the wheel = 37.5 J

genius_generous answered 1 year ago

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