Question

If the rotational speed of a crank of radius 50 cm is 100 RPM and the angular acceleration is 50 rad/s², then the tangential acceleration of the crank will be:

1. 50 m/s²
2. 2.5 m/s²
3. 25 m/s²
4. 0.25 m/s²

Answer 1

Correct Answer - Option 3 : 25 m/s²

Concept:

Tangential acceleration (at):

• It acts along the tangent to the circular path in the plane of the circular path.
• Mathematically Tangential acceleration is written as

\(\overrightarrow {{a_t}} = \vec \alpha \times \vec r \)

Where α = angular acceleration and r = radius

Calculation:

Given:

α = Angular acceleration = 50 rad/s2

r = radius of crank = 50 cm = 0.5 m

Tangential Acceleration at = rα

∴ at = rα = 50 × 0.5 = 25 m/s²