Angular Momentum & Newton's Second Law: Videos & Practice Problems

A 1.5 kg stone is launched horizontally with a velocity of 14.0 m/s at the top of a 10 m high cliff (point A). A recording camera is located on the ground below at a point 15 m from the base of the cliff (point B). Determine the magnitude and direction of the stone's angular momentum relative to the camera at the moment it is launched.

You are strolling around one evening when a 50 g marble is launched horizontally at 15.0 m/s from a 12 m high point in a tall building (point A). Weight is the only force acting on the stone during the flight. Calculate the magnitude and direction of the rate of change of the stone's angular momentum about your feet (point B) the moment it is launched.

A cylindrical ring with a mass M and a radius R has a delicate cord coiled around it. One end of the cord is secured while the ring descends vertically from a stationary position, uncoiling the cord as it goes. Calculate the angular momentum of the ring about its center of mass as it varies with time.

A cylindrical disc with a mass M and a radius R has a delicate thread coiled around it. One end of the thread is secured while the disc descends vertically from a resting position, uncoiling the thread as it goes. What is thread tension as a function of time?

A meteorological mast, used for measuring wind speed and atmospheric data, has a mass of 120 kg and stands 25 m tall. This mast is supported by three guy-wires, each attached at 120° intervals around the mast's base. To assess the failure modes, an analysis is conducted on the scenario where one of the guy-wires breaks. The mast would then rotate about its base opposite the broken wire. Determine the tip speed of the mast as a function of its tilt angle θ relative to the vertical by applying the rotational dynamics equation $\frac{d\vec{L}}{dt}=\vec{τ}_{ext}$. Hint: Approximate the tower as a tall thin rod.

Cricket bats are designed to efficiently transfer energy to the ball, hitting it from the 'sweet spot' where the bat experiences pure rotational motion about the grip. From its handle end, find the sweet spot, $x_{s}$, of the cricket bat shown in the figure. The linear mass density of the bat can be described by $(0.56 + 3.6x^2)$ kg/m, with $x$ in meters from the handle end. The total length of the bat is 1.2 m. The optimal point for rotation should be 15 cm from the handle end. Hint: Consider where the center of mass of the bat might be located.

What is the correct expression for the rotational version of Newton's second law?

What is the formula for the moment of inertia of a point mass?

A fan rotates at 300 RPM. What is its angular velocity in radians per second?

What is the angular momentum of a 2 kg point mass rotating at a radius of 3 m with an angular velocity of 4 rad/s?

A torque is applied in the clockwise direction to a rotating flywheel which initially rotates counterclockwise. How does this affect the angular momentum of the flywheel?

A rotating platform with a moment of inertia of 8 kg m^2 is initially spinning at 20 rad/s. If a negative torque of 16 N m is applied, how long will it take for the platform to stop?

What is the effect of applying a negative torque to a rotating object?

A 5 kg mass is attached to a 2 m long string and rotated in a circle. Calculate the moment of inertia of the mass about the axis of rotation.

If an object has a constant angular momentum but an increasing torque is applied, what can be inferred about the system?

What is the moment of inertia of a 3 kg mass located 4 m from the axis of rotation?

A machine part rotates at 1200 RPM. What is its angular velocity in radians per second?

A rotating object has a moment of inertia of 10 kg m^2 and an angular velocity of 5 rad/s. If the angular velocity triples, what is the new angular momentum?

A gyroscope is spinning with a counterclockwise angular velocity. If a clockwise torque is applied, what happens to the angular momentum vector of the gyroscope?

A CD with a moment of inertia of 0.1 kg m^2 spins at 30 rad/s. If a torque of -0.5 N m is applied, how long will it take for the CD to stop?