Question

Most gasoline engines in today's automobiles are belt driven. this means that the crankshaft, a rod which rotates and drives the pistons, is timed to the camshaft, the mechanism which actuates the valves, by means of a belt. starting from rest, assume it takes t = 0.0100 s for a crankshaft with a radius of r1 = 4.75 cm to reach 1250 rpm. if the belt does not stretch or slip, calculate the angular acceleration a2 of the larger camshaft, which has a radius of r2 = 9.50 cm, during this time period.

Answer 1

To calculate the angular acceleration of a camshaft in a belt-driven engine system, first determine the angular velocity of the crankshaft and then use the ratio of their radii to find the camshaft's angular velocity. Finally, divide this by the time taken to reach that velocity to get the angular acceleration.

Step-by-step explanation:

The student question pertains to calculating the angular acceleration of a camshaft in an automobile engine where it is belt-driven and directly related to the crankshaft's rotation. The camshaft has a larger radius (r2 = 9.50 cm) compared to the crankshaft's radius (r1 = 4.75 cm). Since the belt does not stretch or slip, the angular velocities of the two shafts will be directly proportional to their radii. Knowing the time (t = 0.0100 s) taken for the crankshaft to reach 1250 RPM and its radius, we can use the relationship of angular velocities (ω) to calculate the angular velocity of the camshaft and thereafter find the angular acceleration (a2) considering the system's behavior from rest.

To find the angular acceleration of the camshaft, we start by calculating the angular velocity of the crankshaft (ω1) in rad/s and use the ratio of the radii (r1/r2) to find the angular velocity of the camshaft (ω2). Knowing that angular acceleration is the change in angular velocity over time, we can then use the formula a2 = ω2 / t to find the angular acceleration of the camshaft.