30.00 kg girl riding on the outer edge of a large merry-go-round with a 10.00 m diameter has a rotational kinetic energy of 20.00 J. Find the girl’s moment of inertia relative to the axis of rotation and find the number of revolutions the merry-go-round makes per minute.

A 34 kg hoop of radius 1.3 m, initially rotating at 301 revolutions per minute, is brought smoothly to a stop in 20 s. What is the average power (in Watts) associated with the force that brings the hoop to a stop?

An electric motor exerts a constant torque of τ=10N⋅mτ=10N⋅m on a grindstone mounted on its shaft; the moment of inertia of the grindstone is I=2.0kg⋅m2I=2.0kg⋅m2. If the system starts from rest, find the work done by the motor in 8.0 ss and the kinetic energy at the end of this time. What was the average power delivered by the motor?     SOLUTION SET UP AND SOLVE We want to use W=τΔθW=τΔθ to find the total work done and then divide that by the time interval Δt=8.0sΔt=8.0s to find the average power (work per unit time). But first we need to find the total angle ΔθΔθ (in radians) through which the grindstone turns. The angular acceleration αα is constant, so we can use τ=Iατ=Iα to find αα and then apply the formulas for constant angular acceleration. The angular acceleration is α=τI=10N⋅m2.0kg⋅m2=5.0rad/s2α=τI=10N⋅m2.0kg⋅m2=5.0rad/s2 For constant angular acceleration, θ=θ0+ω0t+12αt2=0+0+12(5.0rad/s2)(8s)2=160radθ=θ0+ω0t+12αt2=0+0+12(5.0rad/s2)(8s)2=160rad The total work…

Consider a basketball player spinning a ball on the tip of a finger. If a player performs 1.95 J of work to set the ball spinning from rest, at what angular speed ? will the ball rotate? Model a basketball as a thin-walled hollow sphere. For a men's basketball, the ball has a circumference of 0.749 m and a mass of 0.624 kg .