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High School Physics : Using Circular Motion Equations

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Example Question #56 : Circular Motion

A 2.2kg object is moving in a perfect circle with a radius of 3.1m and has a linear momentum of $35\frac{kg*m}{s}$ .

What is the centripetal force on the object?

Possible Answers:

129.36N

81.65N

15.91N

395.19N

179.63N

Correct answer:

179.63N

Explanation:

Newton's second law states that F=ma . We know the mass of the object, but we need to find the centripetal acceleration to calculate the centripetal force.

Centripetal acceleration is equal to the tangential velocity squared over the radius:

$a_c=\frac{v^2}{r}$

We know the radius, but we need to find the linear velocity. Fortunately, that's contained in the linear momentum. We know both the momentum and the mass, so we can find the linear velocity.

p=m*v

$35\frac{kg*m}{s}=(2.2kg)v$

$\frac{35\frac{kg*m}{s}}{2.2kg}=v$

$15.91\frac{m}{s}=v$

Use the linear velocity and the radius in the previous equation to solve for the centripetal acceleration.

$a_c=\frac{v^2}{r}$

$a_c=\frac{(15.91\frac{m}{s})^2}{3.1m}$

$a_c=\frac{253.128\frac{m^2}{s^2}}{3.1m}$

$a_c=81.65\frac{m}{s^2}$

Use the centripetal acceleration in Newton's second law, along with the mass, to calculate the centripetal force.

F_c=ma_c

$F_c=2.2kg*81.65\frac{m}{s^2}$

F_c=179.63N

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Example Question #51 : Circular Motion

A baseball has an angular velocity of $88\frac{rad}{s}$ . If the baseball reaches the plate 0.45s after the pitcher releases it, what is the angular displacement of the ball?

Possible Answers:

$44\: rad$

$2.83\: rad$

$39.6\: rad$

$248.8\: rad$

Correct answer:

$39.6\: rad$

Explanation:

The formula for angular displacement with no angular acceleration is $\theta=\omega*t$ .

Plug in our given values.

$\theta=\omega*t$

$\theta=88\frac{rads}{s}*0.45s$

$\theta =39.6\: rad$

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Example Question #41 : Using Circular Motion Equations

A baseball batter swings and misses at a baseball. If the length from his shoulder to the end of the bat is 1.6m , the bat has a mass of 1.1kg , and the bat moves with a linear velocity of $18.3\frac{m}{s}$ , what is the angular momentum generated?

Possible Answers:

21.0J*s

32.21J*s

10.39J*s

16.54J*s

0.03J*s

Correct answer:

32.21J*s

Explanation:

Angular momentum is the product of linear momentum times the lever arm:

L=p*r

Expand this equation by using the formula for linear momentum.

p=mv

L=mv*r

We are given the length of the lever arm (radius), the mass of the bat, and the linear velocity of the swing. Using these values, we can solve for the angular momentum.

L=mv*r

$L=(1.1kg)(18.3\frac{m}{s})(1.6m)$

L=32.21J*s

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Example Question #51 : Circular Motion

A child swings a pail of water in a circle, using her shoulder as the pivot point. If the child's arm is 0.8m long and the pail of water has a linear momentum of $1.67\frac{kg\cdot m}{s}$ , what is the angular momentum of the pail of water?

Possible Answers:

$1.3\ \frac{kg\cdot m^2}{s}$

$0.87\ \frac{kg\cdot m^2}{s}$

$1.07\ \frac{kg\cdot m^2}{s}$

$2.1\ \frac{kg\cdot m^2}{s}$

$2.23\ \frac{kg\cdot m^2}{s}$

Correct answer:

$1.3\ \frac{kg\cdot m^2}{s}$

Explanation:

Angular momentum is equal to the linear momentum times the radial arm.

L=r*p

Since the pivot point of the child is the shoulder, the radial arm is the child's arm length. We are given this length, as well as the linear momentum, allowing us to solve for the angular momentum.

$L=(0.8m)(1.67\frac{kg\cdot m}{s})$

$L=1.3\frac{kg\cdot m^2}{s}$

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Example Question #51 : Circular Motion

A 0.02kg disc has a radius of 0.11m and is thrown horizontally. If it has an angular velocity of $3.2\frac{rad}{s}$ , what is the angular momentum of the disc?

$I_{disc}=\frac{1}{2}MR^2$

Possible Answers:

$1.42*10^{-4}\ \frac{kg\cdot m^2}{s}$

$3.872*10^{-4}\ \frac{kg\cdot m^2}{s}$

$7.04*10^{-5}\ \frac{kg\cdot m^2}{s}$

$3.52*10^{-3}\ \frac{kg\cdot m^2}{s}$

$2.58*10^{-3}\ \frac{kg\cdot m^2}{s}$

Correct answer:

$3.872*10^{-4}\ \frac{kg\cdot m^2}{s}$

Explanation:

The angular momentum of an object is the moment of inertia times the angular velocity:

$L=I\omega$

We can find our moment of inertia using the given formula:

$I_{disc}=\frac{1}{2}MR^2$

Plug in the given mass and radius.

$I_{disc}=\frac{1}{2}(0.02kg)(0.11m)^2$

$I_{disc}=1.21*10^{-4}\ kg\cdot m^2$

Using the value of the moment of inertia and the given angular velocity, we can calculate the angular momentum.

$L=I\omega$

$L=(1.21*10^{-4}\ kg\cdot m^2)(3.2\frac{rad}{s})$

$L=3.872*10^{-4}\ \frac{kg\cdot m^2}{s}$

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Example Question #61 : Circular Motion

A 2kg ball rolls around the edge of a circle with a radius of 1.0m . If it has a centripial force of acting upon it, what is its speed?

Possible Answers:

$1\frac{m}{s}$

$2\frac{m}{s}$

$8\frac{m}{s}$

$4\frac{m}{s}$

$16\frac{m}{s}$

Correct answer:

$2\frac{m}{s}$

Explanation:

Centripetal force is the force that constantly moves the object towards the center; it is what keeps the object moving in a circle rather than flying off tangentially to the circle.

The formula for force is F_c=ma_c .

Since we know the mass and the force, we can find the accleration.

F_c=ma_c

8N=(2kg)a_c

$\frac{8N}{2kg}=a_c$

$4\frac{m}{s^2}=a_c$

Centripetal acceleration is given by the formula $a_c=\frac{v^2}{r}$ , where is the perceived tangential velocity and is the radius of the circle.

Plug in the given values and solve for the velocity.

$4\frac{m}{s^2}=\frac{v^2}{(1m)}$

$1m*4\frac{m}{s^2}=v^2$

$4\frac{m^2}{s^2}=v^2$

$\sqrt{4\frac{m^2}{s^2}}=\sqrt{v^2}$

$2\frac{m}{s}=v$

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High School Physics : Using Circular Motion Equations

Study concepts, example questions & explanations for High School Physics

All High School Physics Resources

Example Questions

Example Question #56 : Circular Motion

Example Question #51 : Circular Motion

Example Question #41 : Using Circular Motion Equations

Example Question #51 : Circular Motion

Example Question #51 : Circular Motion

Example Question #61 : Circular Motion

All High School Physics Resources

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