Hannah is running around the curve of a track in lane 1 (radius 17.3 m) at a con

ID: 1329594 • Letter: H

Question

Hannah is running around the curve of a track in lane 1 (radius 17.3 m) at a constant angular velocity

of 0.4 rad/s. Sasha is running around the curve in lane 8 (radius 34.6 m) with a constant angular

velocity of 0.3 rad/s. (a) Which runner has a greater tangential velocity? (b) Is Hannah’s angular

acceleration greater than, less than, or the same as Sarah’s? (c) Is Hannah’s centripetal (a.k.a. radial)

acceleration greater than, less than, or the same as Sarah’s? (3 pts)

a) Runner with the greater tangential velocity:

b) Hannah’s angular acceleration is (circle one) greater than/less than/the same as Sarah’s

c) Hannah’s centripetal acceleration is (circle one) greater than/less than/the same as Sarah’s

***answer in significant digits and determine magnitude or direction if neccessarry

here,

radius of lane1 , r1 = 17.3 m

radius of lane 8 , r8 = 34.6 m

constant angular velocity of hananah , wh = 0.4 rad/s

constant angular velocity of Sasha , wh = 0.3 rad/s

(a)

tangential velocity of Hannah , vh = r1 *wh

vh = 17.3 * 0.4

vh = 6.92 m/s

tangential velocity of Sarah , vs = r8 *ws

vs = 34.6 * 0.3

vs = 10.38 m/s

Sarah has a greater tangential velocity

(b)

both moves at constant angular speed , therefore angulat accelration of both is zero

(c)

Hannah centripital accelration , ah = vh^2/r1

ah = 2.768 m/s^2

Sarah centripital accelration , as = vs^2/r8

as = 10.38^2 /34.6

as = 3.114 m/s^2

Hannah centripital accelration is less than as Sarah's.

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