Question

A Greenville Utility worker is using a 10 lb sledgehammer behind Ward as part of the construction. Keeping his wrist straight, he swings the sledgehammer through 85° of elbow extension with each swing. His forearm is 40 cm long, and the sledgehammer is 0.8 m long.

a. Find the linear displacements of his hands and the head of the sledgehammer

b. Find the angular displacements of his hands and the head of the sledgehammer

c. Find the linear velocity of his hands and the head of the sledgehammer

d. Find the angular velocity of his hands and the head of the sledgehammer

Answer 1

Let, length of forearm  

Length of the sledgehammer

Angle moved in a swing

a) linear displacement of hand is the length of chord subtending an angle at the center of circle with radius .

Hence, linear displacement of arm

linear displacement of the hammer head is the length of chord subtending an angle at the center of circle with radius .

Hence, linear displacement of hammer head is  

b) The angular displacement of both the hand and the sledgehammer are same and equal to

c). Linear velocity of hands

Linear velocity of hammer head is

d) Angular velocity of hands and the hammer head are same and equal to

Note: c),d) can be calculated if the time is given.