Answer:
0.4 m/s²
Step-by-step explanation:
From the question given above, the following data were obtained:
Mass (m) = 1 kg
Radius (r) = 0.2 m
Angular speed (w) = 20 rad/sec
Time (t) = 10 s
Tangential acceleration (aₜ) =?
Next, we shall determine the angular acceleration (a) of the sphere. This can be obtained as follow:
Angular speed (w) = 20 rad/sec
Time (t) = 10 s
Angular acceleration (a) =?
a = w/t
a = 20/10
a = 2 rad/s²
Finally, we shall determine the tangential acceleration (aₜ) of the sphere. This can be obtained as follow:
The tangential acceleration (aₜ) and the angular acceleration (a) are related according to the equation:
Tangential acceleration (aₜ) = Angular acceleration (a) × Radius (r)
aₜ = ar
With the above formula, we can obtain the tangential acceleration (aₜ) as follow:
Radius (r) = 0.2 m
Angular acceleration (a) = 2 rad/s²
Tangential acceleration (aₜ) =?
aₜ = ar
aₜ = 2 × 0.2
aₜ = 0.4 m/s²
Therefore, the tangential acceleration is 0.4 m/s²