A high-speed flywheel in a motor is spinning at 450 rpmrpm when a power failure suddenly occurs. The flywheel has mass 36.0 kgkg and diameter 80.0 cmcm. The power is off for 25.0 ss, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 160 complete revolutions

1. At what rate is the flywheel spinning when the power comes back on?Express your answer in radians per second.

2. How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on?

3. How many revolutions would the wheel have made during this time?

An advertisement claims that a centrifuge takes up only 0.127 mm of bench space but can produce a radial acceleration of 2200 gg at 5000 rev/minrev/min.

1. Calculate the required radius of the centrifuge

A basketball (which can be closely modeled as a hollow spherical shell) rolls down a mountainside into a valley and then up the opposite side, starting from rest at a height H0H0 above the bottom. In (Figure 1), the rough part of the terrain prevents slipping while the smooth part has no friction. Neglect rolling friction and assume the system's total mechanical energy is conserved.

How high, in terms of H0H0, will the ball go up the other side?

Ho Rough Smooth