Q: A $$2\ \mathrm{kg}$$ object is suspended $$1.5\ \mathrm{m}$$ from a pivot. What is the torque due to gravity about the pivot?

$$\tau = 29.4\ \mathrm{N \cdot m}$$

Q: A steel wire of length $$2\ \mathrm{m}$$ and cross-sectional area $$1 \times 10$$^{-6}$$\ \mathrm{m^2$}$$ stretches by $$1\ \mathrm{mm}$$ under a load. If Young's modulus for steel is $$2 \times 10$$^{11}$$\ \mathrm{N/m^2$}$$, what is the force applied?

$$F = 1 \times 10$$^{6}$$\ \mathrm{N}$$

Q: A diver of mass $$70\ \mathrm{kg}$$ stands at the end of a $$3\ \mathrm{m}$$ long diving board. What is the torque about the base of the board due to the diver's weight?

$$\tau = 2058\ \mathrm{N \cdot m}$$

Question 1

A solid disk of mass $$2\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m}$$ starts from rest and is acted upon by a constant torque of $$1\ \mathrm{N \cdot m}. $$What is the angular acceleration $$\alpha of $$the disk?

Accepted Answer

$$\alpha = 2.0\ \mathrm{$$rad/s^2$$}$$

Question 2

A wheel rotates with a constant angular acceleration. If it starts from rest and reaches an angular velocity of $$10\ \mathrm{rad/s} in$$ $$5\ \mathrm{s}$$, what is the angular displacement during this time?

Accepted Answer

$$	heta = 50\ \mathrm{rad}$$

Question 3

A $$3\ \mathrm{kg}$$ mass is attached to a $$0.4\ \mathrm{m}$$ long massless rod and rotated in a horizontal circle about one end. What is the moment of inertia of the system about the axis of rotation?

Accepted Answer

$$I = 0.48\ \mathrm{kg \cdot m^2$}$$

Question 4

A $$2\ \mathrm{kg}$$ object is suspended $$1.5\ \mathrm{m}$$ from a pivot. What is the torque due to gravity about the pivot?

Accepted Answer

$$	au = 29.4\ \mathrm{N \cdot m}$$

Question 5

A seesaw is $$4\ \mathrm{m}$$ long and has a $$30\ \mathrm{kg}$$ child sitting $$1.5\ \mathrm{m}$$ from the pivot on one side. Where should a $$40\ \mathrm{kg}$$ child sit on the other side to balance the seesaw?

Accepted Answer

$$1.125\ \mathrm{m}$$

Question 6

A $$0.5\ \mathrm{kg}$$ mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}. If $$the spring is stretched by $$0.1\ \mathrm{m}$$, what is the force exerted by the spring?

Accepted Answer

$$F = 20\ \mathrm{N}$$

Question 7

A steel wire of length $$2\ \mathrm{m}$$ and cross-sectional area $$1 	imes 10$$^{-6}$$\ \mathrm{m^2$}$$ stretches by $$1\ \mathrm{mm}$$ under a load. If Young's modulus for steel is $$2 	imes 10$$^{11}$$\ \mathrm{N/m^2$}$$, what is the force applied?

Accepted Answer

$$F = 1 	imes 10$$^{6}$$\ \mathrm{N}$$

Question 8

A $$0.2\ \mathrm{kg}$$ ball moving at $$5\ \mathrm{m/s}$$ collides elastically with a stationary $$0.2\ \mathrm{kg}$$ ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 9

A $$0.1\ \mathrm{kg}$$ hockey puck is hit with a force of $$20\ \mathrm{N}$$ for $$0.05\ \mathrm{s}. $$What is the change in momentum of the puck?

Accepted Answer

$$1\ \mathrm{kg \cdot m/s}$$

Question 10

A $$1\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object at rest. What is their final velocity after the collision?

Accepted Answer

$$1\ \mathrm{m/s}$$

Question 11

A gymnast of mass $$50\ \mathrm{kg}$$ stands on a balance beam $$5\ \mathrm{m}$$ long, supported at its ends. If the gymnast stands $$1\ \mathrm{m}$$ from the left end, what is the upward force exerted by the right support?

Accepted Answer

$$F = 100\ \mathrm{N}$$

Question 12

A $$0.5\ \mathrm{kg}$$ mass is attached to a string and swung in a horizontal circle of radius $$0.8\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is its angular velocity?

Accepted Answer

$$\omega = 2\ \mathrm{rad/s}$$

Question 13

A $$0.2\ \mathrm{kg}$$ mass is attached to a spring and oscillates with a period of $$0.9\ \mathrm{s}. $$What is the frequency of oscillation?

Accepted Answer

$$f = 1.11\ \mathrm{Hz}$$

Question 14

A $$0.3\ \mathrm{kg}$$ ball is dropped from a height of $$2\ \mathrm{m}$$ and bounces straight up to a height of $$1.5\ \mathrm{m}. $$What is the magnitude of the impulse delivered to the ball by the floor?

Accepted Answer

$$J = 2.7\ \mathrm{kg \cdot m/s}$$

Question 15

A uniform beam of length $$6\ \mathrm{m}$$ and mass $$20\ \mathrm{kg} is $$supported horizontally at its ends. A $$60\ \mathrm{kg}$$ person stands $$2\ \mathrm{m}$$ from the left end. What is the force exerted by the right support?

Accepted Answer

$$F = 200\ \mathrm{N}$$

Question 16

A $$0.5\ \mathrm{kg}$$ disk of radius $$0.2\ \mathrm{m}$$ spins at $$10\ \mathrm{rad/s}. $$What is its angular momentum?

Accepted Answer

$$L = 0.05\ \mathrm{kg \cdot m^2$/s}$$

Question 17

A diver of mass $$70\ \mathrm{kg}$$ stands at the end of a $$3\ \mathrm{m}$$ long diving board. What is the torque about the base of the board due to the diver's weight?

Accepted Answer

$$	au = 2058\ \mathrm{N \cdot m}$$

Question 18

A $$0.4\ \mathrm{kg}$$ mass is attached to a string and swung in a circle of radius $$0.5\ \mathrm{m} at$$ $$6\ \mathrm{rad/s}. $$What is the tangential acceleration if the angular acceleration is $$2\ \mathrm{$$rad/s^2$$}$$?

Accepted Answer

$$a_t = 1.0\ \mathrm{m/s^2$}$$

Question 19

A $$0.3\ \mathrm{kg}$$ mass is attached to a spring and oscillates with amplitude $$0.2\ \mathrm{m}. If $$the maximum force exerted by the spring is $$6\ \mathrm{N}$$, what is the spring constant?

Accepted Answer

$$k = 30\ \mathrm{N/m}$$

Rotational Motion, Equilibrium, and Momentum: Study Notes

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