The Question is from NEET guide , and it was created by the author VENKATESWARARAO

Question

A wheel rotates with a constant angular velocity. Which of the following statements is true about a point on the rim of the wheel?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [A]
## CONCEPT FRAMEWORK
	**Primary Concept**: Circular Motion
	**Related Topics**: Angular Velocity, Tangential Speed, Centripetal Acceleration, Angular Acceleration
	**Prerequisites**: Understanding of rotational motion and its relationship to linear motion.
## SOLUTION PATHWAY
**Given Information**:
	* The wheel rotates with a constant angular velocity.
**Method & Steps**:
	1.	**Analyze Angular Velocity**:
		Reasoning: Constant angular velocity means the rate of rotation is not changing.
		Formula/Rule: $\omega = constant$
	2.	**Analyze Tangential Speed**:
		Reasoning: Tangential speed is related to angular velocity and radius.
		Formula/Rule: $v = r\omega$
		Working: Since $r$ is constant (rim of the wheel) and $\omega$ is constant, $v$ is also constant.
		Key Point: Constant angular velocity implies constant tangential speed for a point at a fixed radius.
	3.	**Analyze Tangential Acceleration**:
		Reasoning: Tangential acceleration is the rate of change of tangential speed.
		Formula/Rule: $a_t = \frac{dv}{dt}$
		Working: Since $v$ is constant, $\frac{dv}{dt} = 0$, so $a_t = 0$
	4.	**Analyze Angular Acceleration**:
		Reasoning: Angular acceleration is the rate of change of angular velocity.
		Formula/Rule: $\alpha = \frac{d\omega}{dt}$
		Working: Since $\omega$ is constant, $\frac{d\omega}{dt} = 0$, so $\alpha = 0$
	5.	**Analyze Centripetal Acceleration**:
		Reasoning: Centripetal acceleration is required for circular motion.
		Formula/Rule: $a_c = \frac{v^2}{r} = r\omega^2$
		Working: Since $v$ and $\omega$ are constant and non-zero, $a_c$ is also constant and non-zero.
		Key Point: Centripetal acceleration is always present in uniform circular motion.
	6.	**Conclusion**:
		Result: Only the tangential speed is constant.
		Verification: All other options contradict the given conditions.
 ## OPTION ANALYSIS
[A] ✓: Its tangential speed is constant. This is correct because $v = r\omega$, and both $r$ and $\omega$ are constant.
[B] :x: Its tangential acceleration is non-zero. This is incorrect because the tangential speed is constant, so the tangential acceleration is zero.
[C] :x: Its angular acceleration is non-zero. This is incorrect because the angular velocity is constant, so the angular acceleration is zero.
[D] :x: Its centripetal acceleration is zero. This is incorrect because there is centripetal acceleration for any circular motion.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing tangential and centripetal acceleration. Centripetal acceleration is always present in circular motion, while tangential acceleration is only present if the speed changes.
		2.[Error 2]: Thinking that constant angular velocity means no acceleration.  Centripetal acceleration is always present in circular motion even with constant angular speed
	**Quick Tips**:
		1.[Helpful shortcut]: If angular velocity is constant, tangential speed is constant, tangential acceleration is zero, and angular acceleration is zero.
		2.[Memory aid]: Remember the relationship: $v=r\omega$ and $a_c = r\omega^2$

VENKATESWARARAO · Answer

The correct Option is "Its tangential speed is constant."

VENKATESWARARAO · Answer

Its tangential acceleration is non-zero.

VENKATESWARARAO · Answer

Its angular acceleration is non-zero.

VENKATESWARARAO · Answer

Its centripetal acceleration is zero.

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