In an experiment, a mass m = 40 gm, attached to a string wrapped around the axle of a flywheel and starting from rest, falls through a distance of 147 cm in 3.5 seconds. The diameter of the axle of the flywheel is 12 cm

What is the acceleration of the mass and the angular acceleration of the flywheel?

From kinematics for accelerated motion

s=at^2/2
a=2s/t^2
ε =a/R

To find the acceleration of the mass and the angular acceleration of the flywheel, we can use the formulas related to the motion of objects with rotational motion.

1. First, let's calculate the linear acceleration of the mass using the formula:

a = (2 * Δd) / (t^2)

where a is the linear acceleration, Δd is the distance fallen by the mass, and t is the time taken.

In this case, Δd = 147 cm and t = 3.5 seconds.

Plugging in the values, we get:

a = (2 * 147) / (3.5^2) = 11.38 cm/s^2

Note that we convert the distance from centimeters to meters to maintain consistency with the units of acceleration.

Therefore, the linear acceleration of the mass is 0.1138 m/s^2.

2. Next, let's calculate the angular acceleration of the flywheel using the following formula:

α = a / r

where α is the angular acceleration, a is the linear acceleration, and r is the radius of the flywheel.

In this case, the radius is half the diameter, so r = 12 cm / 2 = 6 cm.

Converting the radius to meters, we get r = 0.06 m.

Plugging in the values, we get:

α = 0.1138 / 0.06 = 1.8967 rad/s^2

Therefore, the angular acceleration of the flywheel is 1.8967 rad/s^2.