Rotational Motion Archives • Page 4 of 4 • Nerd Notes

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What we found:

A pulley system consists of two blocks of mass \( 5 \) \( \text{kg} \) and \( 10 \) \( \text{kg} \), connected by a rope of negligible mass that passes over a pulley of radius \( 0.1 \) \( \text{m} \) and mass \( 2 \) \( \text{kg} \). The pulley is free to rotate about its axis. The system is released from rest, and the block of mass \( 10 \) \( \text{kg} \) starts to move downwards. Assuming that the coefficient of kinetic friction between the pulley and the rope is \( 0.2 \), and neglecting air resistance, determine

The boy is sitting at a distance d1 from the fulcrum, and the girl is sitting at a distance d2 from the fulcrum, with d1 > d2. The seesaw is level, with the two ends at the same height. What is the minimum mass of the seesaw that will keep it balanced with the two children sitting on it?

A seesaw is balanced on a fulcrum, with a boy of mass M1 sitting on one end and a girl of mass M2 sitting on the other end. The seesaw is a uniform plank of length L and mass M. The fulcrum is located at the midpoint of the plank.

A uniform solid cylinder of mass M and radius R is initially at rest on a frictionless horizontal surface. A massless string is attached to the cylinder and is wrapped around it, as shown in the figure below. The string is then pulled with a constant force F, causing the cylinder to rotate about its center of mass. After the cylinder has rotated through an angle θ, what is the kinetic energy of the cylinder (in terms of F and θ)?

A uniform solid sphere of mass M and radius R is placed on a frictionless horizontal surface. A massless string is wrapped around the sphere and is pulled with a force F. The string makes an angle of θ with the horizontal. What is the minimum value of the coefficient of static friction between the sphere and the surface required for the sphere to start rolling without slipping?

A sphere of mass \( M \) and radius \( r \), and rotational inertia \( I \) is released from the top of an inclined plane of height \( h \). The surface has considerable friction. Using only the variables mentioned, derive an expression for the sphere’s center of mass velocity.

A system consists of two small disks, of masses \( m \) and \( 2m \), attached to ends of a rod of negligible mass of length \( 3x \). The rod is free to turn about a vertical axis through point \( P \). The first mass, \( m \), is located \( x \) away from point \( P \), and therefore the other mass, of \( 2m \), is \( 2x \) from point \( P \). The two disks rest on a rough horizontal surface; the coefficient of friction between the disks and the surface is \( \mu \). At time \( t = 0 \), the rod has an initial counterclockwise angular velocity \( \omega_i \) about \( P \). The system is gradually brought to rest by friction. Derive expressions for the following quantities in terms of \( \mu \), \( m \), \( x \), \( g \), and \( \omega_i \).

A ice skater that is spinning in circles has an initial rotational inertia Ii. You can approximate her shape to be a cylinder. She is spinning with velocity ωi. As she extends her arms she her rotational inertia changes by a factor of x and her angular velocity changes by a factor of y. Which one of the following options best describe x and y.

A child of mass \( 3 \) \( \text{kg} \) rotates on a platform of \( 10 \) \( \text{kg} \). They start walking towards the center while the platform is rotating. Which of the following could possibly decrease the total angular momentum of the child-platform system?

Find the following three values using just rotational kinematics. A ball rolls down a 1.5-meter long incline from rest to 3.2 m/s. The ball has a 16.0 cm radius. Find the angular acceleration of the ball. A CD player spins at 7329 rpm. It starts from rest and has an acceleration of 419 rad/s2. How long does it take to reach full speed? A rotating object has a uniform angular acceleration of 5.15 rad/s2. How long does it take to speed up from 3.33 rad/s to 33.3 rad/s?