Question

We have learned that Torque is equal to a force that is perpendicular to a radius (displacement); however, I just cannot grasp one of the study questions we received:

A hammer thrower accelerates the hammer (mass = 7.30 kg) from rest within four full turns (revolutions) and releases it at a speed of 30.0 m/s. Assuming a uniform rate of increase in angular velocity and a radius of 1.50 m, calculate the following answers.

(a)the angular acceleration: 7.96 rad/s2

(b) the (linear) tangential acceleration: 11.94 m/s2

(c) the centripetal acceleration just before release: 600 m/s2

(d) the net force being exerted on the hammer by the athlete just before release: 4380 N

(e) the angle of this force with respect to the radius of the circular motion is___

So basically, I have answered the angular acceleration, tangential acceleration, centripetal acceleration and the net force, but I cannot determine the angle. Thanks!

Answer 1

You know the tangential and centripetal acceleration so it's good to use these directions as base. And you know that the direction of the force is the same as the acceleration. Meaning, you have the direction of the force in the plane the hammer is rotating . In this same plane you know the direction of the radius: it's centripetal . Now you just calculate the angle between and