Rotational Motion Speed at the top of the loop

In summary, the speed at the top of a loop in rotational motion is calculated using the equation v = √(rg), where v is the speed, r is the radius of the loop, and g is the acceleration due to gravity. The speed at the top is directly proportional to the radius of the loop, meaning that as the radius increases, the speed also increases. The mass of an object does not affect its speed at the top of a loop in rotational motion, as it is only dependent on the radius and acceleration due to gravity. The speed at the top can be greater than the speed at the bottom, as it is dependent on the radius while the speed at the bottom is dependent on the height. If the radius is decreased
  • #1
physgrl
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0

Homework Statement



12. A motorcycle travels around a vertical 12 m radius loop. What is its speed at the top of the loop if the normal force exerted by the seat on the driver is equal to ¼ of his weight?

a. 7 m/s

b. 8.1 m/s

*c. 9.4 m/s

d. 15 m/s

e. 88 m/s

Homework Equations



F=ma
W=mg
T=F-W
a=v2/r

The Attempt at a Solution



I did (1/4)W=m(v2/r)-W and I got 12.1 m/s
 
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  • #2
I get the same answer as you.
 

1. How is the speed at the top of a loop in rotational motion calculated?

The speed at the top of a loop in rotational motion can be calculated using the equation v = √(rg), where v is the speed, r is the radius of the loop, and g is the acceleration due to gravity.

2. What is the relationship between speed and radius at the top of a loop in rotational motion?

The speed at the top of a loop in rotational motion is directly proportional to the radius of the loop. This means that as the radius increases, the speed also increases.

3. How does the mass of an object affect its speed at the top of a loop in rotational motion?

The mass of an object does not affect its speed at the top of a loop in rotational motion. This is because the speed is only dependent on the radius of the loop and the acceleration due to gravity, not the mass of the object.

4. Can the speed at the top of a loop in rotational motion be greater than the speed at the bottom?

Yes, the speed at the top of a loop in rotational motion can be greater than the speed at the bottom. This is because the speed at the top is dependent on the radius of the loop, while the speed at the bottom is dependent on the height of the loop.

5. What happens to the speed at the top of a loop in rotational motion if the radius is decreased?

If the radius of the loop in rotational motion is decreased, the speed at the top will also decrease. This is because the equation for speed at the top of a loop involves taking the square root of the radius, so a smaller radius will result in a smaller speed.

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