This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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...GJ. Step 7: Calculate the resulting angle of twist . = 1424.3 Nm × 2 m(70 × 10^9 Pa) × (7.468 × 10^-7 m^4) = (2848.6)/(52276) rad ≈ 0.05449 rad Converting to degrees: _deg = 0.05449 rad × (180^)/( rad) ≈ 3.12^ The resulting angle of twist of the shaft is 0.0545 rad or 3.12^. Q6. a) Define the following terms and state their relations i) Radian: A radian is a unit of angular measure. It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. The relationship between radians and degrees is 2 radians = 360^. ii) Linear and angular velocity: • Linear velocity (v) is the rate of change of an object's position along a straight path, measured in meters per second (m/s). • Angular velocity () is the rate of change of angular displacement, measured in radians per second (rad/s). • Relation: For a point on a rotating object at a distance r from the axis of rotation, the linear velocity is related to the angular velocity by the formula v = r. iii) Linear and angular acceleration: • Linear acceleration (a) is the rate of change of linear velocity, measured in meters per second squared (m/s^2). • Angular acceleration () is the rate of change of angular velocity, measured in radians per second squared (rad/s^2). • Relation: For a point on a rotating object at a distance r from the axis of rotation, the linear acceleration is related to the angular acceleration by the formula a = r. Q6. b) The speed of the shaft increases uniformly from 300 revolutions per minute in 10 sec. Find the angular acceleration correct to 3 significant figures. The phrasing "increases uniformly from 300 revolutions per minute in 10 sec" is ambiguous. We will assume it means the shaft increases its speed uniformly from rest to 300 revolutions per minute in 10 seconds. Given: Initial angular velocity _0 = 0 rev/min (assumed from rest) Final angular velocity _f = 300 rev/min Time t = 10 s Step 1: Convert the final angular velocity from revolutions per minute to radians per second. _f = 300 revmin × 2 rad1 rev × 1 min60 s _f = (300 × 2)/(60) rad/s = 10 rad/s _f ≈ 31.4159 rad/s Step 2: Calculate the angular acceleration using the kinematic equation _f = _0 + t. Since _0 = 0: = (_f)/(t) = 10 rad/s10 s = rad/s^2 ≈ 3.14159 rad/s^2 Step 3: Round the angular acceleration to 3 significant figures. ≈ 3.14 rad/s^2 The angular acceleration is 3.14 rad/s^2 $. Send me the next one 📸