please be detailed You are consulting for an amusement park that wants to build

Question

please be detailed

You are consulting for an amusement park that wants to build a new "Rotor" ride. In order to increase capacity, they would like to build a unit with a 17.7-ft diameter. The Rotor should provide a centripetal acceleration of 3g. What must be the angular speed in revolutions per minute (rpm)?

A spherical object with a moment of inertia of 0.504mr2starts from rest rolling down a 2.25-m high incline. If the sphere is rolling without slipping, what is its linear speed at the bottom of the incline?(Answer with at least three significant figures.)

A spherical object with moment of inertia 0.56mr2rolls without slipping down an incline. At the bottom of the incline, what fraction of its total kinetic energy is rotational kinetic energy? (Answer in percent; use % as units.)

Explanation / Answer

since it rolls without slipping work done by friction is 0
so we can apply energy conservation
mgh=(m*v*v/2)+(i*w*w/2) (i=moment of inertia w=angular velocity)
i for sphere=m*r*r/5
w=v/r in case of pure rolling
10*(2.1*sin25)=(v*v/2)+(v*v/10)
8.87*5/3=v*v
v=3.84m/s
a)w=3.84/.04
=96.14 rad/sec
b)fraction=(1/10)/((1/2)+(1/10))
1/6

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.