Rotation of Of a Rigid Object, Angular Momentum, Static Equilibrium
A bicycle has wheels 67.3cm in diameter and pedal cranks that are 17.5cm long. The speed of the wheel is 76.0 rev/min, front sprocket is 15.2cm and the end sprocket is 7cm in diameter.
(a) Calculate the speed of the chain relative to the bicycle frame.
(b) Calculate the angular speed of the bicycle wheels.
(c) Find the speed of the bicycle relative to the road.
Walls of the tire here are 0.635cm thick, the thread has a width of 20cm and uniform thickness of 2.5cm. The entire object has a density of 1.10 * 10^3 kg/m^3. Find the moment of inertia through the center.
There are two blocks attached with a string on a pulley with the mass of the first block greater than the mass of the second block. The blocks are separated by a distance 2h.
(a) Use conservation of energy to find the speeds of the blocks passing each other.
A hanging cylinder has a mass of 0.42kg and the block on the table has a mass of 0.85kg.
The pulley has a mass of 0.35kg, an inner radius of 0.02m and an outer radius of 0.03m.
The coefficient of kinetic friction is 0.25 between the table and the block. The block’s speed toward the pulley is 0.820 m/s.
(a) Use methods involving energy to find its speed after it has moved 0.7m closer to the
pulley.
(b) Find the angular speed of the pulley when the block is 0.7m closer to the pulley.
A block with mass m is dangling down with a rope attached to it. The rope raps around a spool with radius r and then is attached to a support object. When the block is released drops down with velocity v and the distance h. Prove that the moment of inertia of the rotating apparatus. mr^2(2gh/v^2 - 1)
The string of a grass trimmer has 100g of cord with a density of 10 g/m in a cylindrical spool that has a diameter being 18.0 cm and the inside diameter being 3.0 cm. The cord extends out 16 cm.
(a) The speed of the trimmer is goes from 0 to 2,500 rev/min in 0.215 seconds. Find the
average power of the head by the trimmer.
(b) The trimmer spins at 2,000 rev/min and he grass exerts a force of 7.65N. Find the
power of the head.
Find the moment of inertia of a thin rod that has a length L and mass M about an axis perpendicular to the rod going through the center of mass.
