Answer: a) 0.000093 kg.m²
b) height of the can not required
Explanation:
It is placed at rest on its side, initial velocity = 0
s = ½ a t²
3 = ½ a 1.5²
a = 2.667 m/s²
torque T = f R = μ m g R cos Φ
according to Newton's second law of rotational motion,
T = I α = I (a/R) = μ m g R cos Φ
μ = I a/(R²m g cos Φ)
∑F = m a
m g sin Φ - μ m g cos Φ = m a
canceled all m, and remember that μ = I a/(R²m g cos Φ)
g sin Φ - I a/(R²m g cos Φ) g cos Φ = a
g sin Φ - I a/(R²m) = a
9.8 sin 24° - I (2.667)/(0.0319² * 0.205) = 2.667
3.86 - I x 2.667/0.000208 = 2.667
3.86 - 12822 x I = 2.667 m
I = 3.86 - 2.667 / 12822 = 1.193 / 12822 = 0.000093 kg.m²
