Question

A boulder of mass 20 kg and radius 20 cm rolls down a hill 15 m high from rest. What is its angular momentum when it is halfway down the hill?

(a) Angular momentum is conserved, so it is zero.
(b) Angular momentum is mv, where v is the velocity.
(c) Angular momentum is Iω, where I is the moment of inertia and ω is the angular velocity.
(d) Angular momentum depends on the mass and radius only.

Answer 1

To find the angular momentum of the boulder when it is halfway down the hill, we need to use the formula for angular momentum, which is given by option (c) Angular momentum is Iω, where I is the moment of inertia and ω is the angular velocity.

Step-by-step explanation:

To find the angular momentum of the boulder when it is halfway down the hill, we need to use the formula for angular momentum, which is given by option (c) Angular momentum is Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia for a rolling object, such as a boulder, is given by I = (2/5)MR2, where M is the mass of the object and R is the radius. The angular velocity can be calculated using the equation ω = v/R, where v is the velocity. At halfway down the hill, the boulder has reached a velocity, v, which can be calculated using the equation v = √(2gh), where g is the acceleration due to gravity and h is the height. Plugging the values into the formulas, we can find the angular momentum.

Alternatively, option (b) Angular momentum is mv, where v is the velocity, can be used to find the angular momentum at halfway down the hill. However, this formula applies to point masses, and a rolling boulder cannot be considered as a point mass. Therefore, it is better to use the formula given in option (c).