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An 15-cm-long bicycle crank arm, with a pedal at one end, is attached to a 25-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 65 rpm to 91 rpm in 11 s .
A) What is the tangential acceleration of the pedal?
B)What length of chain passes over the top of the sprocket during this interval? Need units as well

Sagot :

The tangential acceleration and length of chain of rocket is 0.5708 and 9.4m respectively.

  • Any object's rotational motion experiences tangential acceleration, which is the rate at which the tangential velocity varies.
  • When an object is moving, it behaves in a tangential direction.
  • When an object is moving in a circle, the tangential velocity also operates in the same direction. Only when an object follows a circular path does tangential acceleration take place.
  • In cases where the body is rotating more quickly, it is positive; in cases where it is slowing down, it is negative; and in cases where the body is rotating uniformly throughout the orbit, it is zero.

Initial angular velocity, w = 65rpm = 65(rad/s = 6.594rad/s

Final angular velocity, w = 91rpm = 91(rad/s = 9.734rad/s

time taken, t= 11s

Then let total radians covered in this much time be 0 and angular acceleration be a, using equations of motion.

a). 9.734 6.59  and 0.2854rad/s

= (9.734)(6.594) +2(0.2854)/3

A=0.5708

b).Then radius of sprocket R= diameter/2= (25/2)cm E =12.5cm

Then length of chain passes over the top of sprocket in this intervalis

r= (0-12.5m)(89/ 821)

r=9.4m

To study about tangential acceleration -

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