Angular acceleration Quiz 1

Question 1

If the angular displacement of a ball performing rotational motion in terms of time is given by $$	heta =7.5{{t}^{3}}-2\pi {{t}^{2}}$$, determine the magnitude of its angular acceleration at $$t=5	ext{ }\sec $$.

Accepted Answer

$$225-4\pi $$

Answer

$$4\pi -225$$

Answer

$$525-4\pi $$

Answer

$$4\pi -525$$

Question 2

A wheel of $$1	ext{ m}$$ radius is observed to be spinning at a constant angular velocity. It takes $$2	ext{ sec}$$ for the wheel to complete one revolution. An unknown force acts upon the wheel for $$5	ext{ sec}$$ and now, it is observed that the angular velocity of the wheel is $$1.57	ext{ rad }{{	ext{s}}^{-1}}$$. What is the magnitude of angular acceleration linked with the wheel?

Accepted Answer

$$	ext{0}	ext{.31 rad }{{	ext{s}}^{-2}}$$

Answer

$$	ext{1}	ext{.31 rad }{{	ext{s}}^{-2}}$$

Answer

$$	ext{3}	ext{.1 rad }{{	ext{s}}^{-2}}$$

Answer

$$	ext{13}	ext{.1 rad }{{	ext{s}}^{-2}}$$

Question 3

If the angular acceleration and the force acting per unit length on a merry-go-round are $$3.2	ext{ rad }{{	ext{s}}^{-2}}$$ and $$2.48	ext{ N m}$$, how difficult is it to stop the merry-go-round?

Accepted Answer

$$0.775	ext{ kg }{{	ext{m}}^{2}}$$

Answer

$$5.75	ext{ kg }{{	ext{s}}^{2}}$$

Answer

$$5.75	ext{ kg }{{	ext{m}}^{2}}$$

Answer

$$0.755	ext{ kg }{{	ext{s}}^{2}}$$

Question 4

A wasp is walking along the circumference of a round crockery plate with an angular velocity of $$\dfrac{\pi }{4}	ext{ rad }{{	ext{s}}^{-1}}$$. The wasp stops walking when it reaches half of its journey. Evaluate the wasp’s angular acceleration.

Accepted Answer

$$-\dfrac{\pi }{32}	ext{ rad }{{	ext{s}}^{-2}}$$

Answer

$$\dfrac{\pi }{17}	ext{ rad }{{	ext{s}}^{-2}}$$

Answer

$$-\dfrac{\pi }{54}	ext{ rad }{{	ext{s}}^{-2}}$$

Answer

$$\dfrac{\pi }{26}	ext{ rad }{{	ext{s}}^{-2}}$$

Question 5

The ratio of force of an object of mass $$	ext{7 g}$$ in rectilinear motion to its torque in radial motion is $$3:4$$. Determine the angular acceleration of the object if its angular mass in radial motion and acceleration in rectilinear motion are $$0.5	ext{ kg }{{	ext{m}}^{2}}$$ and $$2	ext{ m }{{	ext{s}}^{-2}}$$, respectively.

Accepted Answer

$$37.33	imes {{10}^{-3}}	ext{ rad }{{	ext{s}}^{-2}}$$

Answer

$$66.23	imes {{10}^{-2}}	ext{ rad }{{	ext{s}}^{-2}}$$

Answer

$$35.32	imes {{10}^{-4}}	ext{ rad }{{	ext{s}}^{-2}}$$

Answer

$$26.62	imes {{10}^{-1}}	ext{ rad }{{	ext{s}}^{-2}}$$