A small block with a mass m1 = 4 kg is located at the edge of a disk with a mass

Question

A small block with a mass m1 = 4 kg is located at the edge of a disk with a mass of m2 = 20 kg and radius of R = 0.25 m as shown in the figure below. Static friction between the block and the surface of the disk keeps the block stationary with respect to the disk as the disk rotates about an axis through the center of the disk and perpendicular to the surface of the disk (the dashed line in the figure). If the angular speed of the rotation is 6 rad/s, what is the rotational kinetic energy (in J) of the system?

Explanation / Answer

m1 = 4 kg, m2 = 20 kg, R = 0.25 m, = 6 rad/s,

I = m1R2 + m2R2/2 = (m1 + m2/2)R2

the rotational kinetic energy (in J) of the system

= I2/2 = (m1 + m2/2)R22/2 = 15.75 J

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