1. The cylindrical tub of a washing machine has a radius of 34 cm. During the spin cycle, the wall of the tub rotates with a tangential speed of 5.5
m/s. Calculate the centripetal acceleration of the clothes sitting against the tub.
2. A record with a diameter of 30 cm is played at 33 rpm. What is the tangential velocity at the edge of the record?
3. In the movie 2001: A Space Odyssey, a rotating space station with a diameter of 300 m provides “artificial gravity”. What tangential velocity must the space station have so people in the rim feel 1 g of gravity? How many revolutions per minute is this?
The distance around the circumference is
So the time it takes to complete 1 revolution is
So in one minute, it completes
4. A 30 kg child plays on a swing. The swing is suspended from a horizontal bar 3 m above the ground by a pair of ropes 2.5 meters long. If the child’s maximum height is 2 m above the ground,
and the minimum height is ½ meter above the ground, how heavy does the child feel when the swing reaches its lowest point?
The child will feel his own weight (178 N) plus the centripetal force caused by his circular motion.
We know m, the mass of the child is 30 kg. We know r, the length of the ropes suspending the swing. But we don’t yet know v, the tangential velocity at the bottom of the swing.
The child’s tangential velocity at the bottom can be found by equating his potential energy at the bottom with his change in potential energy.
Plugging this into our formula for centripetal force gives us
3. To simulate gravity, a hypothetical space station spins. With what tangential velocity must the space station have so people in the rim feel 1 g of gravity? How many revolutions per minute is this?