Need help finding the angular speed and the rotational kinetic energy A solid un

Question

Need help finding the angular speed and the rotational kinetic energy

A solid uniform-density sphere is tied to a rope and moves (without spinning) in a circle with speed 8 m/s. The distance from the center of the circle to the center of the sphere is 1.5 m, the mass of the sphere is 11 kg, and the radius of the sphere is 0.77 m. (a) What is the angular speed w? angular speed = 10.38961039 X radians/s (b) What is the rotational kinetic energy of the sphere? K rot= j (c) What is the total kinetic energy of the sphere? K total = j

Explanation / Answer

part a)

w = v/d

w = 8/1.5 = 5.33 m/s

part b )

KErot = 1/2 * Iw^2

I = 2/5 * MR^2

KErot = 1/2 * (2/5 * MR^2) *w^2

KErot = 37.056 J

part c )

KEtot = 1/2 * mv^2 + KErot

KEtot = 389.056 J

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