During a discus throw, Arthur's arm rotates 25 rad/s, and the discus is 1.5 m from the axis of rotation when he releases it. Blake's arm rotates 30 rad/s, and the discus is 1.1 m from the axis of rotation when he releases it. Whose discus throw is most likely to be farther

Answer: Arthur

Explanation: This is a question under the concept of circular motion.

We will model the distance away from the axis of rotation as the radius of the circular motion (r).

for Arthur,

Angular speed (ω) = 25 rad/s

Radius = 1.5m

The linear (tangential) velocity is gotten as

v = ωr

v = 25 * 1.5

v = 37.5 m/s

For Blake

ω = 30 rad/s and r = 1.1m

v = ωr

v = 30 * 1.1

v = 33 m/s

Since the linear speed of Arthur's throw is faster than that of Blake's, it implies that the discus of Arthur will travel a father distance than that of Blake.

Given:

Arthur:

Angular velocity, ωa = 25 rad/s

Radius, ra = 1.5 m

Blake:

Angular velocity, ωb = 30 rad/s

Radius, rb = 1.1 m

Tangential velocity, v = ω * r

va = 25 * 1.5

= 37.5 m/s

vb = 30 * 1.1

= 33 m/s

At the rate the discus travels through a distance in 1 second, velocity with the greater magnitude will cover more distance. That is, the discuss thrown by arthur will be farther than that thrown by blake.