Assignment:
Question 1. A bicycle wheel consist of a rim ( radius R = 0. 40 m ) and essintially massless spokes. Soppose we mount the bycle wheel on the wall. so that the wheel is parallel to the wall. Is it free to spin around its center, but not freee to translate. A very light string is wrapped around the rim and a mass m + 0. 80 kg is attached to the end of the string. The mass is then released and falls 1.5 m in 0.78 s
- Determine the mass of the rim.
- Determine the final angular velocity of the wheel
- Through how many rotations did the wheel spin?
- Calculate the work done by the mass on the wheel.
Question 2. A solid cylinder of mass M and raduis R is rolling without slipping towards a semicircular track. The cylinder's rotation velocity around its central axis is omega 0 The track is attached to the floor. The radius of the semicircle is a. Note that a>>R. the cylinder roll up the track without slipping until it looses contact with the track at point P.
- Derive the moment of inertia for the cylinder about itel center axis
- Determine the cylinder's center - of - madd speed when it reaches point Q
- Determine the height of point P in term of g, R , a, and omega 0