Question

Imagine a monkey is sitting inside a barrel turned on its side. A cruel elephant pushes the barrel down a hill and the monkey starts to roll inside the barrel. This particular monkey gets motion sickness, and an outside observer has noticed that if the monkey spins more than once per second, the monkey will likely vomit. The barrel rolls perfectly down the slope (without slipping) and the outside observer calculates the angular acceleration of the barrel to be 1.2rad/s2. The barrel has a diameter of 1.5 m.
(a) How long will it take for the monkey to spin fast enough to vomit? (b) How far will the monkey have rolled before vomiting?
(c) How many times will the monkey have made a complete circle before vom- iting?

Answer 1

Hi there!

We can begin by converting "spinning once per second" to angular velocity:

$\frac{1rev}{1s} * \frac{2\pi rad}{1rev} = 2\pi rad/sec$

(a)

As we are given the angular acceleration, we can calculate the time using the following equation:

ωf = ωi + αt

There is an initial angular velocity of 0 rad/sec, so:

ωf = αt

2π/1.2 = t

t = 5.236 sec

(b)

We can use the following rotational kinematic equation to first solve for the angular displacement:

θ = ωit + 1/2αt²

The initial velocity is 0 rad/sec, so plug in values:

θ = 1/2(1.2)(5.236²)

θ = 16.449 rad

Convert to linear distance using the following:

d = θr

d = 1.5m, so r = 1.5/2 = 0.75m

d = 16.449(0.75) = 12.337m

(c)

Find the amount of revolutions by converting radians to revolutions:

$16.449 rad * \frac{1rev}{2\pi rad} = \large\boxed{2.618 rev}$

OR, 2.618 times.