Q4. a) Define i. Couple ii. Torque and state it units b) A pulley is 600mm in diameter and the difference in tension on the two sides of the driving belt is 1.5KN. If the Speed of the pulley is 500 rev/min, determine i.) the torque developed ii. The work done in 3 minutes.

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 $2\pi \text{ radians} = 360^\circ$.

• 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 ($\omega$) 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 $v = r\omega$.

• Linear acceleration ($a$) is the rate of change of linear velocity, measured in meters per second squared (m/s$^2$).
• Angular acceleration ($\alpha$) 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 $a = r\alpha$.

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 $\omega_0 = 0$ rev/min (assumed from rest)
Final angular velocity $\omega_f = 300$ rev/min
Time $t = 10$ s