A merry-go-round has a mass of 1420 kgkg and a radius of 7.35 mm .Part AHow much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.20 ss ? Assume it is a solid cylinder.Express your answer using three significant figures and include the appropriate units.
Question
A merry-go-round has a mass of 1420 kgkg and a radius of 7.35 mm .Part AHow much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.20 ss ? Assume it is a solid cylinder.Express your answer using three significant figures and include the appropriate units.
Solution
To solve this problem, we need to use the formula for the rotational kinetic energy of a solid cylinder, which is (1/2) * I * ω^2, where I is the moment of inertia and ω is the angular velocity.
Step 1: Convert the rotation rate from revolutions per second to radians per second. 1 revolution = 2π radians, so 1 revolution per 7.20 seconds = (2π/7.20) rad/s = 0.872 rad/s.
Step 2: Calculate the moment of inertia (I) for a solid cylinder, which is (1/2) * m * r^2. Given that the mass (m) is 1420 kg and the radius (r) is 7.35 m (note: convert mm to m), we get I = (1/2) * 1420 kg * (7.35 m)^2 = 38,500 kg*m^2.
Step 3: Substitute I and ω into the kinetic energy formula to find the final kinetic energy. KE = (1/2) * 38,500 kg*m^2 * (0.872 rad/s)^2 = 14,600 J.
Since the merry-go-round starts from rest, its initial kinetic energy is 0. Therefore, the net work required to accelerate it to the given rotation rate is equal to the final kinetic energy, which is 14,600 J.
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